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Dual Way Residue Noise Thresholding along with feature preservation
Accepted Manuscript
Dual Way Residue Noise Thresholding along With Feature Preservation Bhawna Goyal , Ayush Dogra , Sunil Agrawal , B.S. Sohi PII: DOI: Reference:
S0167-8655(17)30066-1 10.1016/j.patrec.2017.02.017 PATREC 6755
To appear in:
Pattern Recognition Letters
Received date: Revised date: Accepted date:
2 December 2016 23 February 2017 27 February 2017
Please cite this article as: Bhawna Goyal , Ayush Dogra , Sunil Agrawal , B.S. Sohi , Dual Way Residue Noise Thresholding along With Feature Preservation, Pattern Recognition Letters (2017), doi: 10.1016/j.patrec.2017.02.017
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Highlights A unique method for calculating residue noise has been given. The performance of Weighted bilateral filter on image denoising has been improvised PSNR values higher than state of art denoising techniques have been achieved. The concept of adding the residue calculated via two way denoising can lead to significant improvement in preservation of feature details.
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Dual Way Residue Noise Thresholding along With Feature Preservation a
Bhawna Goyala, Ayush Dograa, Sunil Agrawal and B.S. Sohib a
UIET,Panjab University,Chandigarh-160017,India Chandigarh University, Gharaun, Punjab-140413,India
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Dual Way Residue Noise Thresholding along With Feature Preservation
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ABSTRACT
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It is extensively endorsed that preserving the intrinsic geometrical features of an image is essential while denoising it. With an aim to achieve this several directional image representations have been given in the recent literature. In this paper an efficient denoising scheme using an innovative method of calculating the residue image is being proposed. The residue image is further thresholded to remove excessive noise while recovering fine features and details. The recovered features are added to first stage of denoised image to enhance the information content and visual quality of denoised image. The proposed methodology DWRNT (Dual Way residue noise thresholding) is a combination of various spatial and transforms domain methods. Extensive experimental results and investigations reveal that our method can depict far better performance in terms of both subjective evaluation and objective evaluation than various other state-of-the-art image denoising techniques. In this way the proposed methodology is able to recover feature details of an image thereby reducing information loss along with efficient noise removal. 2012 Elsevier Ltd. All rights reserved.
Corresponding author. Tel.: +91-8894897646; e-mail: [email protected]
ACCEPTED MANUSCRIPT During image transmission and acquisition images tend to get corrupted with noise. Imaging and the high resolution videos have become indispensable parts in the life of people. Applications in context of denoising ranges from daily documentation of occurrences and visual data communication to more solemn ones like surveillance and medical fields [1,2,3]. This has led to ever-growing demand for precise and visually pleasant images. Denoising has emerged as basic step for preprocessing in the field of image fusion object recognition remote sensing, image enhancement and image registration [4,5,6,7]. The noise may get introduced in an image during acquisition phase and also while transporting over a communication channel. Other sources of noises can be during analog to digital conversion processes. The most commonly targeted noise in literature is AWGN (Additive White Gaussian Noise) whose mean is assumed to be zero and standard deviation is known [8,9] and the same issue is being addressed in this paper. Image denoising is basically a trade-off between the removal of the noise and preservation of the image features [10].
A denoised image is a pre-requisite in reading any kind of signal [17]. Image denoising is the most fundamental operation used prior to any kind of image processing. A denoised image is important to obtain accurately aligned and high quality fused images [18-22]. A plethora of image denoising techniques have been proposed so far which includes Wavelets[23], Ridgelet[24], Ripplet[25-27], Curvalet[28,29], Tetrolet[30], Counterlet[31], Wedgelets[32], Shearlets[33], BM3D[34], Bilateral filtering[35], Multiresolution bilateral filtering [36], Weighted Bilateral filtering [37] BLS-GSM [38], LPA-PCA [39], Anisotropic diffusion methods [40], translational invariant Framlets[41]. Various histogram equalisation techniques have also been exploited in context of image densoising [42, 43].The former enlisted parent techniques coupled with Bayes thresholding are able to perform well in the past decade. Gradually during the last five years the focus of denoising techniques have shifted to hybridization of various spatial and transforms domain filters to harness the advantages of both the filters into one technique. In Gaussian/Bilateral filter method noise thresholding (GFMT) the concept of method noise thresholding has been introduced along with a hybrid approach of combining a spatial domain filtering and wavelet thresholding in Bayesian domain [44].
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The basic purpose of image denoising is to restructure a likely estimate of the source image from the distorted image and maintain a balance between the removal of the noise and the feature preservation.
as not to lose the non-noisy coefficients along with non retention of the high amplitude noisy coefficients.
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1. Introduction
There are various non linear and linear methods available for denoising [11]. These non linear and linear methods can be broadly classified in three domains i.e. spatial domain filtering, transform domain filtering and dictionary learning methods [2, 3].
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The spatial domain filtering of a noisy image has proven to be an efficient method when high frequency components have to be removed. Spatial domain filters are based on the convolution process and are hence computationally complex. Frequency domain techniques outperform spatial domain methods due to convolution property of the Fourier transform where multiplication of the spectra is done instead of convolution [12]. The principal idea of transform domain methods is that as the noise is distributed amongst all frequencies, the high frequency smaller coefficients result in noise and the larger components with low frequency are signal values [13]. So most of the frequency domain methods assume low pass filtering to suppress most of the high frequency components with an aim to reconstruct the image. Most of the denoising methodologies and strategies undertake an assumed model for the representation of the image and the noise. The following observations differentiate between the noise and the original signal: (i) the clean and the noisy image show different kind of behaviours in multiresolutional representations (ii) intensity and details of important geometrical features of an image i.e. edges or time structure of a signal over exceed noise signal at low resolutions [14]. In transform domain methods non linear methods are used based on multi resolution analysis. Using transform domain methods image is decomposed into transformed coefficients for instance wavelet coefficients which are compared with a set threshold [15]. If the coefficient value is less than the reference value (threshold value), then that coefficient is reduced to zero in case of hard thresholding or is suppressed to a lower value in case of soft thresholding. There are a variety of thresholding schemes available in literature i.e. Sure Shrink, Visu shrink, Bayes Shrink, Neigh Shrink; Minimal threshold [16]. It requires a huge amount of intuitive knowledge for the selection of the optimal threshold so
In this article a novel idea of Dual Way Residue Noise Thresholding (DWRNT) is being introduced for improved denoising effect. The concept of the proposed scheme is to recover the information loss due to denoising. To achieve this images from two different denoising filters are subtracted from each other to obtain the residue image. This residue image is further thresholded to drop noise pixels and to preserve information pixels. The resultant image is added to previously denoised image. The resultant image so obtained is dually denoised along with additional feature preservation. It is found that the final image is far better in terms of PSNR values and visual quality. The rest of the paper is being organized in different sections. Section 2 discusses the related work based on method noise thresholding and the theoretical background of Weighted Bilateral Filtering (WBF), BM3D and Shearlet transform. Section 3 presents the objective evaluation parameter. Section 4 describes the proposed methodology. Section 5 includes the results and discussions. Finally the article is concluded along with the future scope in Section 6.
2. Related work 2.1 Gaussian/Bilateral Filter Method Noise thresholding (GBFMT) In 2013 B.K Shreyamsha Kumar proposed a denoising scheme based on Gaussian/Bilateral filtering and its method noise thresholding [44]. In this scheme the idea of method noise has been presented. The method noise here refers to the difference between the original image and the denoised image, by certain algorithm. The difference in itself is noise and is called method noise. where MN is the method noise, B is the image initially corrupted with noise and Is is the image obtained by applying a certain denoising algorithm. In GBFMT a noisy image is assumed to be corrupted with Gaussian white additive noise with mean zero and a known variance which can be varied for testing at high and low noise values. The corrupted image is
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Method noise comprises of details and noise. Further the method noise is decomposed into wavelet coefficients and Bayes thresholding is applied. Then the threshold coefficients are added with outcome of the bilateral filtering. The final image has more details as compared to the filtered image of the alone. There are several other techniques based on method noise thresholding which have been exploited in literature [4548].
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2.2 Weighted Bilateral Filtering
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The bilateral filter is known to be quite effective and established method for image denoising. In [35,37] a simple pre-processing step of employing a box filters ahead of bilateral filtering to substantially improve the performance of the bilateral filtering (robust bilateral filtering) was presented. The Weighted Bilateral Filtering (WBF) is obtained by combining the original bilateral filter and its modification in a weighted fashion with an aim to minimize the MSE (Mean Square Error). The working of the bilateral filtering involves one edge stopping function (range kernel) and geometric closeness function (spatial kernel). The pixels in an image can be close to each other in two ways i.e. either they are spatially at a very small distance from each other or they have similar pixel intensity values. Bilateral filtering estimates the image representation by averaging both the geometric closeness and intensity value similarity. The function for edge stopping attenuates the filter weights as a function of pixel intensity difference in a directly proportional manner. Mathematically for an image P the bilateral output for a location of pixel m can be calculated as follows [35,37]: ∑
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( )‖) ( )
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‖) is the geometric closeness function (‖ where (‖ ( ) ( )‖) is the edge stopping function, W is defined as normalization constant and is given as ∑
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scanned or searched. The blocks that matched and possessed similarity are piled together to construct a 3D array. In this way the higher correlation amongst the array dimensions in which blocks are piled is shown. By applying decorrelation unitary transform in 3D domain the correlation in the blocks can be depicted which results in a sparsely represented signal in 3D domain [34]. After representing the image sparsely, the noise attenuation is done by applying for example hard thresholding or Weiner filtering on the transform coefficients. The local estimation of the matched blocks constructed by inverse 3D transform results in an image efficiently denoised. The BM3D approach was primarily designed taking into consideration the contamination of the images by Additive White Gaussian Noise. However the earlier versions of BM3D were low on sparsity and thus tend to lower the denoising performance. To further increase the sparsity of the true signal in 3D domain Dabov et al. proposed a generalization of BM3D filter by making use of mutually similar shape adaptive neighbourhoods. These adaptive shape neighbourhoods display local adaptivity to image details and features so that the true signal becomes mostly homogenous. The detailed working algorithm of the BM3D consists of two steps first is to construct a basic estimate and then to construct a final estimate. The blocks similar to each other according to some reference R (closer in distance) are stacked together in a dimension higher than the intial dimension. A 3D transform is applied to the 3D array and noisy coefficients are suppressed using hard thresholding. The estimates are then placed back at their original positions after applying the inverse 3D transform. Now using this basic estimate of the noisy signal the final estimate of true image is calculated. Similar to basic estimate Block matching, collaborative filtering is done for calculation of final estimate. The noisy coefficients are thresholded using Wiener filtering. Further ahead in 2009 to enhance the adaptivity of the preexisting shape adaptive BM3D Dabov et al. introduced PCA (principal component analysis) as a part of the 3D domain. The overall 3D transform is a separable composition of the PCA and a fixed orthogonal 1D transform in third dimension [49,50]. The technique has been further improvised by addressing novel shrinkage criteria which are highly adaptive to the utilized transform.
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filtered using bilateral filtering [35] which tends to average the noise value while preserving the sharp edges or transitions in the image (provided standard deviation of noise is lesser than the edge contrast). Another filter available for image sharpening is Gaussian filter [9]. In case of application of the Gaussian filter the harmonic parts of the image are flattened optimally whereas the edges and textures are smoothed. Now this image obtained by spatial domain filtering i.e. Is is subtracted from the original image B to obtain the method noise. Now this method noise will consist of the noise which has not been removed by filtering as well as the image details which has removed mistakenly as noise [44]. The MN obtained by Gaussian filtering will have strong edges as the edges are preserved in case of bilateral filtering due to range filtering.
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and S is the spatial neighbourhood of m and n belongs to S. The WBF is obtained by a linear combination of Robust Bilateral Filter and Bilateral filter with weights computed to minimize the SURE risk estimate 2.3 Block matching 3D Filtering BM3D is an efficient filtering in 3D transform domain. With the help of a sliding window the similar blocks are
2.4 Shearlet Transform Wavelets have achieved remarkable success in providing optimal approximation for 1-dimensional functions which are continuous piecewise. They are not very effective in optimally representing the multivariate functions such as sharp intensity changes or edges in an image [51]. To overcome such limitations the researchers have introduced several directional representations like composite wavelets, ridgelets, curvelets and counterlets with an aim to obtain subtle representations for such multivariate functions. While devising a transform one has to use a basis element with are more sensitive to directions and have more directions and shapes as compared to the classical wavelets [52]. The limitation of the Curvelet transform is that it has not been generated in the discretization domain also is not able to provide a multiresolution geometry. Moreover the mathematical investigation and implementation is more complex and tedious. Further Counterlets are constructed with basis functions which are elongated [53]. However, counterlets have lesser directional features and also tend to introduce artefacts in denoising and compression.
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For a given value of S and T the Fourier transform of a composite wavelet function is given by [55]: (
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[ ] ( ) By the above listed condition Shearlet is band limited. The parameter i controls the orientation selectivity of ᴪ.
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2.4.1.Non-sub sampled Shearlet Transform
Non-sub sampled Shearlet transform is an exclusive type of discrete Shearlet transform. The major underlying property of NSST which has made it very popular for image processing is its property of invariance to the shifting in the input signal. In context of denoising it is well known that shift variance introduces Gibbs phenomena around singularities i.e. artefacts which are considerably reduced by NSST. The NSST is implemented using Non-sub sampled Pyramid filter banks (NSP) and Non-sub sampled shearing (NSS) filters [55,56]. NSST was introduced by omitting the up and the down sampling. Since the coefficients are not decimated amongst the decomposition levels, the sizes of the sub bands remain as the size of the original input image. Instead of Laplacian pyramids NSST uses 2-D non sub sampled pyramid filter banks. Non sub sampled filter banks has no up sampling and down sampling. NSP tends to create multiple scale decomposition levels of the image into higher values frequency sub-bands Hp and lower values of frequency sub-bands Lp where p=1,2,3,4.........i equal in sizes to the original image.[54-56]
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The objective evaluation metrics calculated for the quality of results so obtained in the context of this article is PSNR (peak signal to noise ratio). PSNR is measured in decibels. Higher is the PSNR value better is the extent of the denoised image so obtained. It is calculated as [2,3,9]: (
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where MSE is the difference or cumulative error between the original and the denoised image[39,41]. Lower is the calculated MSE value better is the result of the denoised image. It is calculated as ∑ [ ( ) ( )] where m and l are the number of columns and rows of the input image respectively. 4. Proposed methodology (DWRNT)
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where ( ) is a mother wavelet function and is appropriately band limited function, S and T are invertible | matrices and | and j, i, k are direction, scale and shift parameters. The matrix T and S are dilation and shear matrices respectively [52]. The Shearlets are obtained by applying shear transformations, translations and anisotropic dilations on a mother function which can be represented in matrix form as [55]
NSS does the filtering of the directions in the space domain using 2D convolution. The use of spatial domain omits the sampling operation and thus possesses induces invariance. NSS decomposes the high frequency bands so obtained by NSP into directional sub bands Hpq q=1,2,3....l. The non sub sampled shearing filters banks are iteratively applied. At each cycle low frequency sub bands are divided into high and low frequency sub bands there by giving multidirectional and multiscale decomposition. More details can be found in [54,55,57].
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Shearlet is a recent transform and is capable of multiresolutional and multiscale represenation. It has depicted its efficacy in providing sparse representations which are optimal for a variety of data e.g. multidimensional data and data with higher number of feature variations. It has shown incredible results in variety of image processing applications such as image enhancement, image fusion, deconvolution etc. Shearlets provide a more flexible tool and is more natural in implementation. The major underlying property of Shearlets is their shift invariance. Shearlets are band limited and compactly supported. The well known mother wavelets are scaled and shifted to obtain standard wavelets. Shearlets are basically a type of composite wavelets having a directional parameter as well. Shearlets helps to provide the multiresolutional analysis [54] The 2D composite wavelet can be written as [55]
The proposed scheme aims at dual way residue noise thresholding (DWRNT) by employing the combination of the Weighted Bilateral filter, NSST and BM3D. A novel method for computing the residue noise and feature details has been introduced in this article. In this work the output of the weighted bilateral filter is optimized by adding the feature details to the bilateral filter output which are obtained by thresholding the residue image resulting from subtraction of two images. In this technique a two way denoising is done to calculate the residue which is further threshold to eliminate the remaining noise and preserve additional feature details such as texture and edges resulting in dual way denoising. The framework for the proposed methodology is illustrated in Fig1. The typical denoising methods are governed by the principle of smoothing of the images. However most of the algorithms tend to over smooth the images. The important edge and texture informed contained in images also gets removed and results in cartoon like images. Our technique is based on the idea that instead of traditional ways of calculating the method noise, the residue comprising of details as well noise is obtained by subtracting the output of the weighted bilateral filter and NSS( Non Sub sampled) inverse transformed image. The test images are shown in Fig2. An image I is contaminated with Additive White Gaussian Noise (AWGN) at standard deviation =10. The noisy images are shown in Fig3. The original image is estimated from the distorted image by employing the Weighted Bilateral Filter and Non-subsampled Shearlet transform individually. As described above Nonsubsampled Shearlet transform due its shear parameters,
ACCEPTED MANUSCRIPT translational factors and dilation metrics results in the multiscale and multidirectional representation of the image. When coupled with hard thresholding the NSST tends to remove the noise in the image, while preserving feature details due to high amount of directional representation.
AWGN =10
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5. Results and discussions The input test images for the present analysis are 256256 Lena, Barbara and MRI which are taken from the internet database and are shown in Fig2. The standard test images Lena and Barbara are chosen to test the performance of the proposed methodology so as to compare with other denoising techniques recently reported in [44,45]. The image is contaminated with Additive White Gaussian Noise (AWGN) at standard deviation =10, which represents the medium value of noise generally found in these images. The noisy images are shown in Fig3. Using our proposed methodology, the noisy image is applied to WBF (weighted bilateral filter) and NSST filters for denoising. The denoised images thus obtained are shown in Fig4 and Fig5. The input image is decomposed into four levels using NSST. The size of the shearing filters is 3*3, 3*3, 4*4, and 4*4 at each decomposition level respectively. The directional filter sizes for each shearing filter at four decomposition levels are 32, 32, 16, and 16. The variance of the noisy signal is computed for all the sub bands and the variance of the noise free signal is estimated. The noisy coefficients are thresholded using hard thresholding [52]. Then the inverse transformed image is obtained as the output of NSST. The residue images calculated after subtracting the outputs of the WBF and NSST are shown in Fig6. Further thresholding of residue images results in images as shown in Fig7. This thresholded image is then added with output of WBF to get final denoised image as shown in Fig 8.
Input image
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which certainly has more detailed features than the WBF output.
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Final denoised image
Fig2. Input test images of Lena, Barbara and MRI (left to Right)
Fig1. Flow chart of the proposed methodology
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On the other hand the Weighted Bilateral Filter tends to retain some amount of noise along with over smoothing of the image. The residue thus calculated by subtracting the output If of the weighted bilateral filter from the output It of NSST , is denoted as Ri i.e. the residue. This residue image is further thresholded with block matching and 3D filtering (BM3D) resulting in recovery of feature details with two step removal of the noisy coefficients. The thresholded residue Rth containing significant feature details and least amount of noise is then added to WBF output. The final output image Id certainly contains higher degree of directional representation, fine features and details than the original output of the weighted bilateral filter . The purpose of dual way denoising is to capture the additional feature representation provided by Shearlet transform and to remove the extra amount of noise. The summation of the WBF output with thresholded residue will give denoised image
Fig3. Noisy images at standard deviation 10
Fig4. Output of Weighted Bilateral Filter for Lena, Barbara and MRI (left to Right)
ACCEPTED MANUSCRIPT PSNR( 31.80) for DWRNT is also higher than GFMT(30.85) and BFMT(31.63), the techniques based on method noise thresholding reported in [44,45 ]. Also the PSNR values for the proposed methodology is higher than the PSNR values outputs of WT, MRBF and BF which are established techniques in terms of denoising. To check the versatility of our method, a medical image MRI (Magnetic Resonance Imaging) has been taken. The NLMNT (Non-local method noise thresholding) , BFMT, WBF and DRWNT (proposed) are also tested on MRI image. The results are compared and presented in Table2.
Fig5. Output of NSST for Lena, Barbara and MRI (left to Right)
Fig6. Residue noise by subtracting output of NSST and WBF for Lena, Barbara and MRI (left to Right)
BFMT WBF NLMNT
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Table2 : PSNR values for denoising techniques on MRI image MRI Image Denoising Technique 256256; =10
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Fig8. Final denoised image for Lena, Barbara and MRI (left to Right)
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To compare the performance of our methodology, a number of denoising techniques like WT (Wavelet Transform), Multiresolution Bilateral filter (MRBF), Bilateral filter (BF), GFMT(Gaussian Filter Method Noise Thresholding), BFMT(Bilateral Filter Method Noise Thresholding), Weighted Bilateral Filter (WBF) have been applied on standard Lena and Barbara images. The PSNR values for final images for all of the techniques have been calculated and are summarized in Table1.
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Table1: PSNR values for denoising techniques on Lena and Barbara Image Lena Barbara Denoising Technique 256256 256256 =10 =10 WT [44] 30.77 29.16 MRBF[44] 31.34 28.99 BF[44] 29.28 24.88 GFMT[44] BFMT[44] WBF[44] DWRNT(proposed)
30.85 31.63 31.32 31.80
29.01 29.16 30.01 30.41
Now as we can see from Table1 that the PSNR value is highest for the proposed methodology (DWRNT) as compared to other techniques. Our technique is able to outperform the output of WBF ( PSNR=31.32) which shows that after adding the thresholded residue the image quality gets increased. The
32.03 31.36 32.65
As it is obvious from Table2 that the PSNR value for our proposed methodology is higher than the PSNR value for WBF. Also our technique is better in terms of PSNR as compared to NLMNT. This improvement may be attributed to the fact that edge information obtained from thresholding of the residue is added to the output of the WBF which gives enhanced feature details and textures. Besides having high PSNR values it can be confirmed from the subjective and visual evaluation of images in Fig8 and Fig4 that results for proposed methodology have enhanced feature details than the output of the WBF. In the proposed methodology DWRNT we have selected one spatial and one transform domain filter to harness the attributes of both the filters. The Shearlet transform due to its properties of shift invariance and multi scale and multi resolution directional representation is able to give a high PSNR value. In the DWRNT a low PSNR image (output of WBF) is subtracted from a high PSNR image (output of NSST). The high amount of intricate features and details which have otherwise being eliminated from the output of the weighted bilateral filter are present in the residue subtracted along with some amount of noise. The residue when further thresholded with BM3D is left with the intricate feature details because of high efficiency of the well known BM3D. The results shown in Table1 and 2 clearly depicts that our proposed methodology is able to give a higher PSNR value than other techniques and the presence of preserved feature details is evident. The scheme suggested in this paper can give high quality image denoising along with the preservation of edges, sharp transitions and gradient information. Especially in the field of medical imaging where presence of image details is vital for diagnosis and treatment of diseases, the DRWNT can provide with high quality denoised image. Further in the field of weather forecasting where images are highly corrupted with sensor noise due to distantly placed cameras and atmospheric pressure, the proposed technique can help to give an image free from noise without losing onto important geometrical feature details. The proposed scheme however shows a higher amount of computational complexity as compared to other denoising techniques because of the intense processing and multilevel cascading schematic .These issues will be looked into in the upcoming work by trying various other types of filters and adaptive thresholding methods.
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Fig 7. Residue threshold with BM3D for Lena, Barbara and MRI (left to Right)
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6. Conclusion
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In this paper a novel image denoising method using dual way residue noise thresholding has been proposed. The performance of the same has been analyzed on the standard test images and compared with state of the art techniques. In this, the alternative and better idea of calculating and thresholding the residue image has been proved to be extremely efficient technique for denoising. The residue image thus calculated is devoid of the unwanted residue noise which is further thresholded thereby recovering the fine details and edges. By introduction of non-separable pyramids and non sub sampled shearing filters in NSST domain, the quality of shift invariance is induced in Shearlet transform which caters the Gibbs phenomena along with feature preservation. The Weighted bilateral filter output augmented with threshold residue results in higher feature details in the final image. So our technique has outperformed the existing methods in terms of PSNR and feature preservation. There is no funding.
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28. Starck, Jean-Luc, Emmanuel J. Candès, and David L. Donoho. "The curvelet transform for image denoising." IEEE Transactions on image processing 11, no. 6 (2002): 670-684. 29. Starck, J-L., Fionn Murtagh, Emmanuel J. Candes, and David L. Donoho. "Gray and color image contrast enhancement by the curvelet transform." IEEE Transactions on image processing 12, no. 6 (2003): 706-717. 30. Krommweh, Jens. "Tetrolet transform: A new adaptive Haar wavelet algorithm for sparse image representation." Journal of Visual Communication and Image Representation 21, no. 4 (2010): 364-374. 31. Do, Minh N., and Martin Vetterli. "The contourlet transform: an efficient directional multiresolution image representation." IEEE Transactions on image processing 14, no. 12 (2005): 2091-2106. 32. Claypoole Jr, Roger L., and Richard G. Baraniuk. "Multiresolution wedgelet transform for image processing." In International Symposium on Optical Science and Technology, pp. 253-262. International Society for Optics and Photonics, 2000. 33. Guo, Kanghui, Gitta Kutyniok, and Demetrio Labate. "Sparse multidimensional representations using anisotropic dilation and shear operators." Wavelets und Splines (Athens, GA, 2005), G. Chen und MJ Lai, eds., Nashboro Press, Nashville, TN (2006): 189-201. 34. Dabov, K., Foi, A., Katkovnik, V. and Egiazarian, K., 2006, February. Image denoising with block-matching and 3D filtering. In Electronic Imaging 2006(pp. 606414-606414). International Society for Optics and Photonics 35. Tomasi, C. and Manduchi, R., 1998, January. Bilateral filtering for gray and color images. In Computer Vision, 1998. Sixth International Conference on(pp. 839-846). IEEE. 36. Zhang, Ming, and Bahadir K. Gunturk. "Multiresolution bilateral filtering for image denoising." IEEE Transactions on Image Processing 17, no. 12 (2008): 2324-2333. 37. Chaudhury, K.N. and Rithwik, K., 2015, September. Image denoising using optimally weighted bilateral filters: A SURE and fast approach. In Image Processing (ICIP), 2015 IEEE International Conference on (pp. 108-112). IEEE 38. Rajaei, B., 2014. An analysis and improvement of the BLS-GSM denoising method. Image Processing On Line, 4, pp.44-70. 39. Zhang, Lei, Weisheng Dong, David Zhang, and Guangming Shi. "Two-stage image denoising by principal component analysis with local pixel grouping." Pattern Recognition 43, no. 4 (2010): 15311549. 40. Maleki, Arian, Manjari Narayan, and Richard G. Baraniuk. "Anisotropic nonlocal means denoising." Applied and Computational Harmonic Analysis35.3 (2013): 452-482 41. Shen, Lixin, Manos Papadakis, Ioannis A. Kakadiaris, Ioannis Konstantinidis, Donald Kouri, and David Hoffman. "Image denoising using a tight frame." IEEE transactions on image processing 15, no. 5 (2006): 1254-1263. 42. Dogra, A., and Sunil Agrawal.” 3-Stage Enhancement Of Medical Images Using Ripplet Transform,high Pass Filters and Histogram Equalization
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Dual Way Residue Noise Thresholding along With Feature Preservation Bhawna Goyal , Ayush Dogra , Sunil Agrawal , B.S. Sohi PII: DOI: Reference:
S0167-8655(17)30066-1 10.1016/j.patrec.2017.02.017 PATREC 6755
To appear in:
Pattern Recognition Letters
Received date: Revised date: Accepted date:
2 December 2016 23 February 2017 27 February 2017
Please cite this article as: Bhawna Goyal , Ayush Dogra , Sunil Agrawal , B.S. Sohi , Dual Way Residue Noise Thresholding along With Feature Preservation, Pattern Recognition Letters (2017), doi: 10.1016/j.patrec.2017.02.017
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Highlights A unique method for calculating residue noise has been given. The performance of Weighted bilateral filter on image denoising has been improvised PSNR values higher than state of art denoising techniques have been achieved. The concept of adding the residue calculated via two way denoising can lead to significant improvement in preservation of feature details.
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Dual Way Residue Noise Thresholding along With Feature Preservation a
Bhawna Goyala, Ayush Dograa, Sunil Agrawal and B.S. Sohib a
UIET,Panjab University,Chandigarh-160017,India Chandigarh University, Gharaun, Punjab-140413,India
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Dual Way Residue Noise Thresholding along With Feature Preservation
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It is extensively endorsed that preserving the intrinsic geometrical features of an image is essential while denoising it. With an aim to achieve this several directional image representations have been given in the recent literature. In this paper an efficient denoising scheme using an innovative method of calculating the residue image is being proposed. The residue image is further thresholded to remove excessive noise while recovering fine features and details. The recovered features are added to first stage of denoised image to enhance the information content and visual quality of denoised image. The proposed methodology DWRNT (Dual Way residue noise thresholding) is a combination of various spatial and transforms domain methods. Extensive experimental results and investigations reveal that our method can depict far better performance in terms of both subjective evaluation and objective evaluation than various other state-of-the-art image denoising techniques. In this way the proposed methodology is able to recover feature details of an image thereby reducing information loss along with efficient noise removal. 2012 Elsevier Ltd. All rights reserved.
Corresponding author. Tel.: +91-8894897646; e-mail: [email protected]
ACCEPTED MANUSCRIPT During image transmission and acquisition images tend to get corrupted with noise. Imaging and the high resolution videos have become indispensable parts in the life of people. Applications in context of denoising ranges from daily documentation of occurrences and visual data communication to more solemn ones like surveillance and medical fields [1,2,3]. This has led to ever-growing demand for precise and visually pleasant images. Denoising has emerged as basic step for preprocessing in the field of image fusion object recognition remote sensing, image enhancement and image registration [4,5,6,7]. The noise may get introduced in an image during acquisition phase and also while transporting over a communication channel. Other sources of noises can be during analog to digital conversion processes. The most commonly targeted noise in literature is AWGN (Additive White Gaussian Noise) whose mean is assumed to be zero and standard deviation is known [8,9] and the same issue is being addressed in this paper. Image denoising is basically a trade-off between the removal of the noise and preservation of the image features [10].
A denoised image is a pre-requisite in reading any kind of signal [17]. Image denoising is the most fundamental operation used prior to any kind of image processing. A denoised image is important to obtain accurately aligned and high quality fused images [18-22]. A plethora of image denoising techniques have been proposed so far which includes Wavelets[23], Ridgelet[24], Ripplet[25-27], Curvalet[28,29], Tetrolet[30], Counterlet[31], Wedgelets[32], Shearlets[33], BM3D[34], Bilateral filtering[35], Multiresolution bilateral filtering [36], Weighted Bilateral filtering [37] BLS-GSM [38], LPA-PCA [39], Anisotropic diffusion methods [40], translational invariant Framlets[41]. Various histogram equalisation techniques have also been exploited in context of image densoising [42, 43].The former enlisted parent techniques coupled with Bayes thresholding are able to perform well in the past decade. Gradually during the last five years the focus of denoising techniques have shifted to hybridization of various spatial and transforms domain filters to harness the advantages of both the filters into one technique. In Gaussian/Bilateral filter method noise thresholding (GFMT) the concept of method noise thresholding has been introduced along with a hybrid approach of combining a spatial domain filtering and wavelet thresholding in Bayesian domain [44].
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The basic purpose of image denoising is to restructure a likely estimate of the source image from the distorted image and maintain a balance between the removal of the noise and the feature preservation.
as not to lose the non-noisy coefficients along with non retention of the high amplitude noisy coefficients.
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1. Introduction
There are various non linear and linear methods available for denoising [11]. These non linear and linear methods can be broadly classified in three domains i.e. spatial domain filtering, transform domain filtering and dictionary learning methods [2, 3].
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The spatial domain filtering of a noisy image has proven to be an efficient method when high frequency components have to be removed. Spatial domain filters are based on the convolution process and are hence computationally complex. Frequency domain techniques outperform spatial domain methods due to convolution property of the Fourier transform where multiplication of the spectra is done instead of convolution [12]. The principal idea of transform domain methods is that as the noise is distributed amongst all frequencies, the high frequency smaller coefficients result in noise and the larger components with low frequency are signal values [13]. So most of the frequency domain methods assume low pass filtering to suppress most of the high frequency components with an aim to reconstruct the image. Most of the denoising methodologies and strategies undertake an assumed model for the representation of the image and the noise. The following observations differentiate between the noise and the original signal: (i) the clean and the noisy image show different kind of behaviours in multiresolutional representations (ii) intensity and details of important geometrical features of an image i.e. edges or time structure of a signal over exceed noise signal at low resolutions [14]. In transform domain methods non linear methods are used based on multi resolution analysis. Using transform domain methods image is decomposed into transformed coefficients for instance wavelet coefficients which are compared with a set threshold [15]. If the coefficient value is less than the reference value (threshold value), then that coefficient is reduced to zero in case of hard thresholding or is suppressed to a lower value in case of soft thresholding. There are a variety of thresholding schemes available in literature i.e. Sure Shrink, Visu shrink, Bayes Shrink, Neigh Shrink; Minimal threshold [16]. It requires a huge amount of intuitive knowledge for the selection of the optimal threshold so
In this article a novel idea of Dual Way Residue Noise Thresholding (DWRNT) is being introduced for improved denoising effect. The concept of the proposed scheme is to recover the information loss due to denoising. To achieve this images from two different denoising filters are subtracted from each other to obtain the residue image. This residue image is further thresholded to drop noise pixels and to preserve information pixels. The resultant image is added to previously denoised image. The resultant image so obtained is dually denoised along with additional feature preservation. It is found that the final image is far better in terms of PSNR values and visual quality. The rest of the paper is being organized in different sections. Section 2 discusses the related work based on method noise thresholding and the theoretical background of Weighted Bilateral Filtering (WBF), BM3D and Shearlet transform. Section 3 presents the objective evaluation parameter. Section 4 describes the proposed methodology. Section 5 includes the results and discussions. Finally the article is concluded along with the future scope in Section 6.
2. Related work 2.1 Gaussian/Bilateral Filter Method Noise thresholding (GBFMT) In 2013 B.K Shreyamsha Kumar proposed a denoising scheme based on Gaussian/Bilateral filtering and its method noise thresholding [44]. In this scheme the idea of method noise has been presented. The method noise here refers to the difference between the original image and the denoised image, by certain algorithm. The difference in itself is noise and is called method noise. where MN is the method noise, B is the image initially corrupted with noise and Is is the image obtained by applying a certain denoising algorithm. In GBFMT a noisy image is assumed to be corrupted with Gaussian white additive noise with mean zero and a known variance which can be varied for testing at high and low noise values. The corrupted image is
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Method noise comprises of details and noise. Further the method noise is decomposed into wavelet coefficients and Bayes thresholding is applied. Then the threshold coefficients are added with outcome of the bilateral filtering. The final image has more details as compared to the filtered image of the alone. There are several other techniques based on method noise thresholding which have been exploited in literature [4548].
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2.2 Weighted Bilateral Filtering
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The bilateral filter is known to be quite effective and established method for image denoising. In [35,37] a simple pre-processing step of employing a box filters ahead of bilateral filtering to substantially improve the performance of the bilateral filtering (robust bilateral filtering) was presented. The Weighted Bilateral Filtering (WBF) is obtained by combining the original bilateral filter and its modification in a weighted fashion with an aim to minimize the MSE (Mean Square Error). The working of the bilateral filtering involves one edge stopping function (range kernel) and geometric closeness function (spatial kernel). The pixels in an image can be close to each other in two ways i.e. either they are spatially at a very small distance from each other or they have similar pixel intensity values. Bilateral filtering estimates the image representation by averaging both the geometric closeness and intensity value similarity. The function for edge stopping attenuates the filter weights as a function of pixel intensity difference in a directly proportional manner. Mathematically for an image P the bilateral output for a location of pixel m can be calculated as follows [35,37]: ∑
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scanned or searched. The blocks that matched and possessed similarity are piled together to construct a 3D array. In this way the higher correlation amongst the array dimensions in which blocks are piled is shown. By applying decorrelation unitary transform in 3D domain the correlation in the blocks can be depicted which results in a sparsely represented signal in 3D domain [34]. After representing the image sparsely, the noise attenuation is done by applying for example hard thresholding or Weiner filtering on the transform coefficients. The local estimation of the matched blocks constructed by inverse 3D transform results in an image efficiently denoised. The BM3D approach was primarily designed taking into consideration the contamination of the images by Additive White Gaussian Noise. However the earlier versions of BM3D were low on sparsity and thus tend to lower the denoising performance. To further increase the sparsity of the true signal in 3D domain Dabov et al. proposed a generalization of BM3D filter by making use of mutually similar shape adaptive neighbourhoods. These adaptive shape neighbourhoods display local adaptivity to image details and features so that the true signal becomes mostly homogenous. The detailed working algorithm of the BM3D consists of two steps first is to construct a basic estimate and then to construct a final estimate. The blocks similar to each other according to some reference R (closer in distance) are stacked together in a dimension higher than the intial dimension. A 3D transform is applied to the 3D array and noisy coefficients are suppressed using hard thresholding. The estimates are then placed back at their original positions after applying the inverse 3D transform. Now using this basic estimate of the noisy signal the final estimate of true image is calculated. Similar to basic estimate Block matching, collaborative filtering is done for calculation of final estimate. The noisy coefficients are thresholded using Wiener filtering. Further ahead in 2009 to enhance the adaptivity of the preexisting shape adaptive BM3D Dabov et al. introduced PCA (principal component analysis) as a part of the 3D domain. The overall 3D transform is a separable composition of the PCA and a fixed orthogonal 1D transform in third dimension [49,50]. The technique has been further improvised by addressing novel shrinkage criteria which are highly adaptive to the utilized transform.
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filtered using bilateral filtering [35] which tends to average the noise value while preserving the sharp edges or transitions in the image (provided standard deviation of noise is lesser than the edge contrast). Another filter available for image sharpening is Gaussian filter [9]. In case of application of the Gaussian filter the harmonic parts of the image are flattened optimally whereas the edges and textures are smoothed. Now this image obtained by spatial domain filtering i.e. Is is subtracted from the original image B to obtain the method noise. Now this method noise will consist of the noise which has not been removed by filtering as well as the image details which has removed mistakenly as noise [44]. The MN obtained by Gaussian filtering will have strong edges as the edges are preserved in case of bilateral filtering due to range filtering.
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and S is the spatial neighbourhood of m and n belongs to S. The WBF is obtained by a linear combination of Robust Bilateral Filter and Bilateral filter with weights computed to minimize the SURE risk estimate 2.3 Block matching 3D Filtering BM3D is an efficient filtering in 3D transform domain. With the help of a sliding window the similar blocks are
2.4 Shearlet Transform Wavelets have achieved remarkable success in providing optimal approximation for 1-dimensional functions which are continuous piecewise. They are not very effective in optimally representing the multivariate functions such as sharp intensity changes or edges in an image [51]. To overcome such limitations the researchers have introduced several directional representations like composite wavelets, ridgelets, curvelets and counterlets with an aim to obtain subtle representations for such multivariate functions. While devising a transform one has to use a basis element with are more sensitive to directions and have more directions and shapes as compared to the classical wavelets [52]. The limitation of the Curvelet transform is that it has not been generated in the discretization domain also is not able to provide a multiresolution geometry. Moreover the mathematical investigation and implementation is more complex and tedious. Further Counterlets are constructed with basis functions which are elongated [53]. However, counterlets have lesser directional features and also tend to introduce artefacts in denoising and compression.
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[ ] ( ) By the above listed condition Shearlet is band limited. The parameter i controls the orientation selectivity of ᴪ.
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2.4.1.Non-sub sampled Shearlet Transform
Non-sub sampled Shearlet transform is an exclusive type of discrete Shearlet transform. The major underlying property of NSST which has made it very popular for image processing is its property of invariance to the shifting in the input signal. In context of denoising it is well known that shift variance introduces Gibbs phenomena around singularities i.e. artefacts which are considerably reduced by NSST. The NSST is implemented using Non-sub sampled Pyramid filter banks (NSP) and Non-sub sampled shearing (NSS) filters [55,56]. NSST was introduced by omitting the up and the down sampling. Since the coefficients are not decimated amongst the decomposition levels, the sizes of the sub bands remain as the size of the original input image. Instead of Laplacian pyramids NSST uses 2-D non sub sampled pyramid filter banks. Non sub sampled filter banks has no up sampling and down sampling. NSP tends to create multiple scale decomposition levels of the image into higher values frequency sub-bands Hp and lower values of frequency sub-bands Lp where p=1,2,3,4.........i equal in sizes to the original image.[54-56]
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The objective evaluation metrics calculated for the quality of results so obtained in the context of this article is PSNR (peak signal to noise ratio). PSNR is measured in decibels. Higher is the PSNR value better is the extent of the denoised image so obtained. It is calculated as [2,3,9]: (
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where MSE is the difference or cumulative error between the original and the denoised image[39,41]. Lower is the calculated MSE value better is the result of the denoised image. It is calculated as ∑ [ ( ) ( )] where m and l are the number of columns and rows of the input image respectively. 4. Proposed methodology (DWRNT)
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where ( ) is a mother wavelet function and is appropriately band limited function, S and T are invertible | matrices and | and j, i, k are direction, scale and shift parameters. The matrix T and S are dilation and shear matrices respectively [52]. The Shearlets are obtained by applying shear transformations, translations and anisotropic dilations on a mother function which can be represented in matrix form as [55]
NSS does the filtering of the directions in the space domain using 2D convolution. The use of spatial domain omits the sampling operation and thus possesses induces invariance. NSS decomposes the high frequency bands so obtained by NSP into directional sub bands Hpq q=1,2,3....l. The non sub sampled shearing filters banks are iteratively applied. At each cycle low frequency sub bands are divided into high and low frequency sub bands there by giving multidirectional and multiscale decomposition. More details can be found in [54,55,57].
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Shearlet is a recent transform and is capable of multiresolutional and multiscale represenation. It has depicted its efficacy in providing sparse representations which are optimal for a variety of data e.g. multidimensional data and data with higher number of feature variations. It has shown incredible results in variety of image processing applications such as image enhancement, image fusion, deconvolution etc. Shearlets provide a more flexible tool and is more natural in implementation. The major underlying property of Shearlets is their shift invariance. Shearlets are band limited and compactly supported. The well known mother wavelets are scaled and shifted to obtain standard wavelets. Shearlets are basically a type of composite wavelets having a directional parameter as well. Shearlets helps to provide the multiresolutional analysis [54] The 2D composite wavelet can be written as [55]
The proposed scheme aims at dual way residue noise thresholding (DWRNT) by employing the combination of the Weighted Bilateral filter, NSST and BM3D. A novel method for computing the residue noise and feature details has been introduced in this article. In this work the output of the weighted bilateral filter is optimized by adding the feature details to the bilateral filter output which are obtained by thresholding the residue image resulting from subtraction of two images. In this technique a two way denoising is done to calculate the residue which is further threshold to eliminate the remaining noise and preserve additional feature details such as texture and edges resulting in dual way denoising. The framework for the proposed methodology is illustrated in Fig1. The typical denoising methods are governed by the principle of smoothing of the images. However most of the algorithms tend to over smooth the images. The important edge and texture informed contained in images also gets removed and results in cartoon like images. Our technique is based on the idea that instead of traditional ways of calculating the method noise, the residue comprising of details as well noise is obtained by subtracting the output of the weighted bilateral filter and NSS( Non Sub sampled) inverse transformed image. The test images are shown in Fig2. An image I is contaminated with Additive White Gaussian Noise (AWGN) at standard deviation =10. The noisy images are shown in Fig3. The original image is estimated from the distorted image by employing the Weighted Bilateral Filter and Non-subsampled Shearlet transform individually. As described above Nonsubsampled Shearlet transform due its shear parameters,
ACCEPTED MANUSCRIPT translational factors and dilation metrics results in the multiscale and multidirectional representation of the image. When coupled with hard thresholding the NSST tends to remove the noise in the image, while preserving feature details due to high amount of directional representation.
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5. Results and discussions The input test images for the present analysis are 256256 Lena, Barbara and MRI which are taken from the internet database and are shown in Fig2. The standard test images Lena and Barbara are chosen to test the performance of the proposed methodology so as to compare with other denoising techniques recently reported in [44,45]. The image is contaminated with Additive White Gaussian Noise (AWGN) at standard deviation =10, which represents the medium value of noise generally found in these images. The noisy images are shown in Fig3. Using our proposed methodology, the noisy image is applied to WBF (weighted bilateral filter) and NSST filters for denoising. The denoised images thus obtained are shown in Fig4 and Fig5. The input image is decomposed into four levels using NSST. The size of the shearing filters is 3*3, 3*3, 4*4, and 4*4 at each decomposition level respectively. The directional filter sizes for each shearing filter at four decomposition levels are 32, 32, 16, and 16. The variance of the noisy signal is computed for all the sub bands and the variance of the noise free signal is estimated. The noisy coefficients are thresholded using hard thresholding [52]. Then the inverse transformed image is obtained as the output of NSST. The residue images calculated after subtracting the outputs of the WBF and NSST are shown in Fig6. Further thresholding of residue images results in images as shown in Fig7. This thresholded image is then added with output of WBF to get final denoised image as shown in Fig 8.
Input image
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which certainly has more detailed features than the WBF output.
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Fig2. Input test images of Lena, Barbara and MRI (left to Right)
Fig1. Flow chart of the proposed methodology
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On the other hand the Weighted Bilateral Filter tends to retain some amount of noise along with over smoothing of the image. The residue thus calculated by subtracting the output If of the weighted bilateral filter from the output It of NSST , is denoted as Ri i.e. the residue. This residue image is further thresholded with block matching and 3D filtering (BM3D) resulting in recovery of feature details with two step removal of the noisy coefficients. The thresholded residue Rth containing significant feature details and least amount of noise is then added to WBF output. The final output image Id certainly contains higher degree of directional representation, fine features and details than the original output of the weighted bilateral filter . The purpose of dual way denoising is to capture the additional feature representation provided by Shearlet transform and to remove the extra amount of noise. The summation of the WBF output with thresholded residue will give denoised image
Fig3. Noisy images at standard deviation 10
Fig4. Output of Weighted Bilateral Filter for Lena, Barbara and MRI (left to Right)
ACCEPTED MANUSCRIPT PSNR( 31.80) for DWRNT is also higher than GFMT(30.85) and BFMT(31.63), the techniques based on method noise thresholding reported in [44,45 ]. Also the PSNR values for the proposed methodology is higher than the PSNR values outputs of WT, MRBF and BF which are established techniques in terms of denoising. To check the versatility of our method, a medical image MRI (Magnetic Resonance Imaging) has been taken. The NLMNT (Non-local method noise thresholding) , BFMT, WBF and DRWNT (proposed) are also tested on MRI image. The results are compared and presented in Table2.
Fig5. Output of NSST for Lena, Barbara and MRI (left to Right)
Fig6. Residue noise by subtracting output of NSST and WBF for Lena, Barbara and MRI (left to Right)
BFMT WBF NLMNT
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Table2 : PSNR values for denoising techniques on MRI image MRI Image Denoising Technique 256256; =10
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Fig8. Final denoised image for Lena, Barbara and MRI (left to Right)
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To compare the performance of our methodology, a number of denoising techniques like WT (Wavelet Transform), Multiresolution Bilateral filter (MRBF), Bilateral filter (BF), GFMT(Gaussian Filter Method Noise Thresholding), BFMT(Bilateral Filter Method Noise Thresholding), Weighted Bilateral Filter (WBF) have been applied on standard Lena and Barbara images. The PSNR values for final images for all of the techniques have been calculated and are summarized in Table1.
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Table1: PSNR values for denoising techniques on Lena and Barbara Image Lena Barbara Denoising Technique 256256 256256 =10 =10 WT [44] 30.77 29.16 MRBF[44] 31.34 28.99 BF[44] 29.28 24.88 GFMT[44] BFMT[44] WBF[44] DWRNT(proposed)
30.85 31.63 31.32 31.80
29.01 29.16 30.01 30.41
Now as we can see from Table1 that the PSNR value is highest for the proposed methodology (DWRNT) as compared to other techniques. Our technique is able to outperform the output of WBF ( PSNR=31.32) which shows that after adding the thresholded residue the image quality gets increased. The
32.03 31.36 32.65
As it is obvious from Table2 that the PSNR value for our proposed methodology is higher than the PSNR value for WBF. Also our technique is better in terms of PSNR as compared to NLMNT. This improvement may be attributed to the fact that edge information obtained from thresholding of the residue is added to the output of the WBF which gives enhanced feature details and textures. Besides having high PSNR values it can be confirmed from the subjective and visual evaluation of images in Fig8 and Fig4 that results for proposed methodology have enhanced feature details than the output of the WBF. In the proposed methodology DWRNT we have selected one spatial and one transform domain filter to harness the attributes of both the filters. The Shearlet transform due to its properties of shift invariance and multi scale and multi resolution directional representation is able to give a high PSNR value. In the DWRNT a low PSNR image (output of WBF) is subtracted from a high PSNR image (output of NSST). The high amount of intricate features and details which have otherwise being eliminated from the output of the weighted bilateral filter are present in the residue subtracted along with some amount of noise. The residue when further thresholded with BM3D is left with the intricate feature details because of high efficiency of the well known BM3D. The results shown in Table1 and 2 clearly depicts that our proposed methodology is able to give a higher PSNR value than other techniques and the presence of preserved feature details is evident. The scheme suggested in this paper can give high quality image denoising along with the preservation of edges, sharp transitions and gradient information. Especially in the field of medical imaging where presence of image details is vital for diagnosis and treatment of diseases, the DRWNT can provide with high quality denoised image. Further in the field of weather forecasting where images are highly corrupted with sensor noise due to distantly placed cameras and atmospheric pressure, the proposed technique can help to give an image free from noise without losing onto important geometrical feature details. The proposed scheme however shows a higher amount of computational complexity as compared to other denoising techniques because of the intense processing and multilevel cascading schematic .These issues will be looked into in the upcoming work by trying various other types of filters and adaptive thresholding methods.
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Fig 7. Residue threshold with BM3D for Lena, Barbara and MRI (left to Right)
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6. Conclusion
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In this paper a novel image denoising method using dual way residue noise thresholding has been proposed. The performance of the same has been analyzed on the standard test images and compared with state of the art techniques. In this, the alternative and better idea of calculating and thresholding the residue image has been proved to be extremely efficient technique for denoising. The residue image thus calculated is devoid of the unwanted residue noise which is further thresholded thereby recovering the fine details and edges. By introduction of non-separable pyramids and non sub sampled shearing filters in NSST domain, the quality of shift invariance is induced in Shearlet transform which caters the Gibbs phenomena along with feature preservation. The Weighted bilateral filter output augmented with threshold residue results in higher feature details in the final image. So our technique has outperformed the existing methods in terms of PSNR and feature preservation. There is no funding.
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