A new MNF–BM4D denoising algorithm based on guided filtering for hyperspectral images

ISA Transactions 92 (2019) 315–324

Contents lists available at ScienceDirect

ISA Transactions journal homepage: www.elsevier.com/locate/isatrans

Practice article

A new MNF–BM4D denoising algorithm based on guided filtering for hyperspectral images ∗

∗

Xu Ping, Chen Bingqiang, Xue Lingyun , Zhang Jingcheng , Zhu Lei, Duan Hangbo Hangzhou Dianzi University, College of Life Information Science & Instrument Engineering, Hangzhou, China

highlights • • • •

A new MNF–BM4D denoising algorithm based on guided filtering is proposed. BM4D denoising performance is improved significantly in the spatial and spectral domain. Minimum Noise Fraction algorithm is introduced to distinguish different bands. Guided filtering technology is used to further improve the denoising performance.

article

info

Article history: Received 20 August 2018 Received in revised form 15 February 2019 Accepted 16 February 2019 Available online 25 February 2019 Keywords: Hyperspectral images BM4D MNF Guided filtering Denoising

a b s t r a c t This paper proposed a new MNF–BM4D denoising algorithm based on guided filtering to improve the denoising performance of the state-of-the-art Block-Matching and 4D filtering(BM4D) algorithm for hyperspectral images in the spatial and spectral domain. BM4D is firstly used to denoise hyperspectral images. Then Minimum Noise Fraction(MNF) algorithm is introduced to distinguish between the main component and the noisy component. Finally, the guided image filtering technology is utilized to further improve the denoising performance. A number of experiments on both simulated and real data are conducted to validate the effective denoising performance of the proposed method. Therefore, the proposed algorithm can be considered as a promising technique for hyperspectral imagery denoising. © 2019 ISA. Published by Elsevier Ltd. All rights reserved.

1. Introduction Hyperspectral remote sensing technology emerged late last century [1], as a new type of remote sensing technology, that has greatly promoted the development of remote sensing technology. Hyperspectral remote sensing images can help discover the unidentifiable substances in traditional images and make great contributions to the direction of earth observation. However, hyperspectral images are subject to noise information in imaging. This not only reduces the visual quality, but also limits the interpretation and analysis accuracy of subsequent images and spectral information extraction [2]. The hyperspectral image noise mainly comes from the sensor itself [3]. The sensors used for hyperspectral images are usually precision instruments. Electromagnetic interference and mechanical vibration both bring noise to the sensors and affect the collection accuracy of hyperspectral images. Therefore, hyperspectral image denoising is of great significance for the data post-analysis. There are mainly ∗ Corresponding authors. E-mail addresses: [email protected] (Xue L.), [email protected] (Zhang J.). https://doi.org/10.1016/j.isatra.2019.02.018 0019-0578/© 2019 ISA. Published by Elsevier Ltd. All rights reserved.

two types of denoising algorithms in hyperspectral images, denoising algorithms in the spatial domain and denoising algorithms in the transform domain. Chen [4] proposed a denoising method for hyperspectral data using wavelet packets and adjacent wavelets shrinking. Bourguignon [5] proposed restoration procedure that operates on each spectrum by minimizing a penalized data-fit criterion, which took the noise spectral distribution into account with additional constraints expressing prior sparsity information in a union of bases. Spectral smoothing filter for removing noise from the hyperspectral data was proposed [6]. Yang [7] put forward a fluorescence spectrum denoising method for low concentration petroleum pollutants combining the empirical mode decomposition(EMD) and the lifting wavelet transform(LWT). Chen [8] brought forward a normalized least mean square(NLMS) adaptive filtering method to deduct the noise from near-infrared spectrum. Stephan [9] proposed hyperspectral denoising method by principal component analysis(PCA). To identify cabbages and weeds by the SAM classification, Zu [10] utilized the minimum noise fraction(MNF) to reduce the noise and decorrelation of hyperspectral data. However, traditional noise reduction algorithms did not take the characteristics of spectral correlation among hyperspectral images into account, which results in poor

316

Xu P., Chen B., Xue L. et al. / ISA Transactions 92 (2019) 315–324

noise reduction. For instance, Atkinson proposed a denoising algorithm that uses the Fourier transform of the spatial domain for wavelet shrinkage transform and spectral domain [11]; Othman created a spatial–spectral domain hybrid noise reduction algorithm that transforms hyperspectral images into spectral differential domains and uses spatial–spectral mixed wavelet threshold denoising [12]; Huo, based on principal component analysis and dictionary learning, adopted sparse representation method and dual tree complex wavelet transform method to remove spatial dimension and spectral dimension noise [13]; Chen [14] proposed a spatial–spectral domain mixing priority algorithm that first denoises the two-dimensional spatial domain images of hyperspectral images, and then denoises the one-dimensional spectral signals corresponding to each pixel in the two-dimensional spatial domain; Yuan [15] put forward an algorithm by incorporating the two-dimensional spatial information and one-dimensional spectral domain information of the hyperspectral images into the constraints of the objective function and adjusting the parameter control threshold; Kumar [16] proposed an image denoising algorithm based on overlapping group sparsity, which made use of orthogonal moments to extract the correlations among the atoms and group them together by extracting the characteristics of the noisy image patches. The above algorithms mainly removed the oscillating noise in the image. In 2005, Buades [17] proposed a non-local mean(NLM) algorithm which estimated the degree of similarity between its own image blocks, then assigns the weight to the estimated values, and finally averages the values of the image blocks according to the weight values. In 2007, Dabov proposed the Block-Matching and 3D filtering(BM3D) denoising method [18], in which matching and grouping of image blocks were performed by a matching algorithm, and the grouped image blocks were stacked into a three-dimensional matrix, and then the three-dimensional matrix was filtered in the three-dimensional transform domain. In 2013, Maggioni proposed the Block-Matching and 4D filtering(BM4D), which is based on a three-dimensional block matching algorithm. The algorithm is similar to the three-dimensional block matching algorithm in that the grouping of image blocks is extended from twodimensional block matching to three-dimensional block matching [19]. Chen brought forward a hyperspectral image denoising algorithm based on principal component analysis and BM4D [20]. The algorithm firstly separates and recomposes the hyperspectral image noise by PCA algorithm, and then uses BM4D algorithm to reduce noise on the transformed image. BM4D is a state-of-the-art algorithm and can be regarded as a well-known benchmark for the hyperspectral imagery denoising, so the improvement of BM4D is quite promising in this research field. In many hyperspectral application, e.g., the plant hyperspectral images, there are always the hyperspectral reflectances of some bands with dramatic changes which includes plenty of key spectral characteristics. Maintaining data high fidelity in these bands is especially important for these hyperspectral applications. Besides, there are always strong noises, which are difficult to be removed, in the beginning and end of the bands of hyperspectral images. BM4D naturally utilizes similar 3-D cubes of voxels which are stacked together to form the 4-D group [21], which leads to difficulty in effectively denoising these bands that are short of similarity in the hyperspectral images. Guided image filtering was proposed by He et al. [22], which introduced a guided image to remove noise. It may not only preserve the image edge and enhance image details, but also reduce the noise of the image effectively. In this paper, guided image filtering is introduced to further improve the denoising performance of BM4D by choosing the optimal band in the BM4D as the guided filter image. MNF is an effective technique for hyperspectral imagery denoising, which can transforms noisy images into output

images with steadily decreasing image quality [23]. MNF can be used to extract the main components in the hyperspectral images by distinguishing strong noisy components. Therefore, combined with BM4D, guided filtering and MNF, a new MNF–BM4D based on guided filtering algorithm is proposed to remove the noise for hyperspectral images effectively. 2. Algorithm 2.1. The MNF-BM4D algorithm based on guided filtering In order to improve the denoising performance of the state-ofthe-art BM4D algorithm for hyperspectral images, especially for those bands with dramatic changes, this paper proposes a new MNF–BM4D denoising algorithm based on guided image filtering. Fig. 1 shows the flow chart of the proposed algorithm. The proposed algorithm can be divided into the MNF transformation, the BM4D algorithm denoising, and the guided image filtering. Firstly, the MNF transformation is performed to reduce the redundant information and distinguish strong noisy bands for hyperspectral images; secondly, the BM4D algorithm is used to denoise hyperspectral images; then the image of the optimal quality is used as the guide image to filter the image; finally, the denoising effects of the denoised hyperspectral images are evaluated in the spatial and spectral domain. The flow of the proposed algorithm can be summarized as follows: (1) MNF transformation is performed on the hyperspectral images to reduce the redundant information and useless bands, and obtain the hyperspectral images with minimum noise separation fraction; (2) First BM4D denoising (a) Image block grouping. In the hyperspectral images, the similar image blocks are found out by the matching algorithm, and then these similar blocks are stacked into a four-dimensional matrix. (b) Hard threshold filtering. First, the three-dimensional matrices are obtained after grouping, then hard threshold filtering is performed in the three-dimensional transform domain, and finally the filtered three-dimensional data is inversely transformed to obtain the estimated values for each block. (c) Aggregation. The weighted average of the estimated values of all the image blocks are used to obtain the first denoising hyperspectral images. (3) Second BM4D denoising (a) Image block grouping. A matching algorithm is applied to the hyperspectral images after the first BM4D denoising to find similar blocks and stack them into a completely new fourdimensional matrix. (b) Wiener filtering. The first four-dimensional matrix obtained from the first BM4D denoising is regarded as the real signal. After the Wiener filter is used to filter it, the invert transformation is done to obtain the estimated values of each image block. (c) Aggregation. The weighted average of the estimated values of all the image blocks are used to obtain the second denoising hyperspectral images. (4) Guided image filtering (a) local mean and local standard deviation (LMLSD) noise estimation method is used to evaluate the quality of hyperspectral images and the optimal band is selected as the guided image. (b) The guided image is used to filter each band to obtain the final denoising hyperspectral images.

Xu P., Chen B., Xue L. et al. / ISA Transactions 92 (2019) 315–324

317

Fig. 1. Flow chart of the proposed algorithm (the bottom half image is modified according to [19]).

2.2. Minimum noise fraction transformation

(5) Diagonalize matrix CD−adj to obtain matrix DD−adj ;

For hyperspectral images, the most common dimensionality reduction algorithm is principal component analysis(PCA) [24]. The algorithm can effectively remove the redundant information of hyperspectral images and reduce the count of the selected bands. However, the algorithm is susceptible to noise. In order to solve this problem, Green proposed the MNF algorithm [25]. The algorithm can distinguish the main information component from the noise information component, which removes the extra noise information and leads to a concentration on the main information components in the hyperspectral image into fewer bands. It effectively reduces the count of selection of redundant bands and improves the denoising effectiveness. The process of the MNF algorithm is as follows: (1) Use the noise covariance matrix in the principal component to evaluate the covariance matrix CN of the noise of hyperspectral images; (2) Diagonalize CN to obtain a diagonal matrix DN ; DN = U T CN U

(1)

where U is an orthogonal matrix composed of CN eigenvectors, and DN is a diagonal matrix composed of CN eigenvalues. (3) Obtain the transformation matrix P and use it in the hyperspectral image Z to obtain transformed hyperspectral data by Q = PZ transformation; P = UDN

−1/2

T

I = P CN P

(2) (3)

where P is the transformation matrix and I is the identity matrix. (4) Transform the matrix CD to obtain the transformed matrix CD−adj ; CD−adj = P T CD P

(4)

where CD is the covariance matrix of the hyperspectral image data Z, and CD−adj is the P-transformed covariance matrix.

DD−adj = V T CD−adj V

(5)

where V is an orthogonal matrix which is composed of the eigenvectors of the matrix CD−adj . (6) Obtain the matrix TMNF after the minimum noise separation transformation. TMNF = PV

(6)

2.3. Guided image filtering Guided image filtering algorithm can improve the image edge and detail recovery ability, so it is mostly used in image denoising and other related fields. The core of the algorithm is to recover the edges and details of the hyperspectral image by selecting the guided image. The guide image filtering process is as follows: (1) p is the hyperspectral images to be denoised, and I is the image with the best signal-to-noise ratio of the hyperspectral images which is regarded as the guided image: qi = ak Ii + bk , ∀i ∈ wk

(7)

qi = pi − ni

(8)

where a and b are linear coefficients, q is the denoised hyperspectral images, i is the band index, and wk is the whole band set. (2) In order to get the coefficients a and b in Eq. (7) and minimize the difference between p and q, Eq. (7) needs to be turned into an optimization problem solving process, that is to minimize the following equation. E (ak , bk ) =

∑ i∈wk

((ak Ii + bk − pi )2 + ε ak 2 )

(9)

318

Xu P., Chen B., Xue L. et al. / ISA Transactions 92 (2019) 315–324

spatial domain and spectral domain of hyperspectral images [28]. It can be expressed as:

(3) Solve Eq. (9) by least square method:

⎞

⎛ 1 ∑

ak = ⎝

|w|

Ii pi − uk pk ⎠ /(σk 2 + ε )

(10)

i∈wk

f˜ (i, j, z ) = af (i, j, z − 1) + bf (i, j, z + 1) + cf (p, z ) + d

b k = p k − ak uk

(11)

regression coefficients, and f(p,z)can be written as follows:

where uk and σk 2 are the mean and variance of I in the sliding window wk , respectively. |w| is the total number of pixels in the sliding window, and pk is the mean of p in the sliding window wk . (4) Calculate q:

⎧ ⎨f (i − 1, j, z ) i > 1 f (p, z ) = f (i, j − 1, z ) i = 1, j > 1 ⎩ null i = 1, j = 1

1 ∑ qi = (ak Ii + bk ) = ai Ii + bi |w| k:i∈k ∑ ∑ 1 1 where ai = |w| k∈wi ak , bi = |w| k∈wi bk .

r (i, j, z ) = f (i, j, z ) = f˜ (i, j, k)

(12)

(18)

Noise variance is written as follows:

σn 2 =

l m ∑ ∑

1 H −4

1

r (i, j, z )2

(19)

1

H=l×m−1 3.1. Different denoising algorithms

3.2. Hyperspectral image quality evaluation methods 3.2.1. Noise evaluation method in the spatial domain Gao proposed the local mean and local standard deviation (LMLSD) method for noise assessment [26]. LMLSD, which is based on edge block elimination, is used to evaluate the noise of real hyperspectral images in the spatial domain. The edge is removed √ by edge detection, and then the image is divided into √ n × n sub blocks. The mean ML and standard deviation DLS of each block can be obtained as follows: ML =

√

n

i

j

DLS = [

(n2

f (i, j, z)

(13)

n n ∑ ∑

1

− 1)

1

(f (i, j, z ) − ML )2 ] 2

i

(14)

j

PSNR value can be obtained as follows: RSN = 20 lg

ML DLS

(20)

The mean gray value of the image is:

Simulated and real data experiments are undertaken to demonstrate the effectiveness of the proposed algorithm for hyperspectral image denoising. To validate the proposed method, some state-of-the-art algorithms, including 3DFFT, NLM, BM3D, and BM4D, are chosen to make comparison with the proposed algorithm. For 3DFFT, the cut-off frequency of the Gaussian filter is set as 25; for NLM, the searching window of each band is set as 7 × 7, and the adjacent window is 3 × 3; for BM3D, the noise standard deviation of each band is chosen as the threshold and the size of match block is set as 8 × 8; for BM4D, the size of a match block is 8 × 8 and the local window is 3 × 3; for the proposed algorithm, the hard-threshold parameter λ4D for BM4D is set as the default value of 2.7 and the parameters of the guided filter are r = 2 and ϵ = 0.0012 . All algorithms were implemented using MATLAB R2014b on a PC equipped with four Intel Core i5-3230 M CPU (at 2.60 GHz) and 4 GB of RAM memory.

√

(17)

After decorrelation:

3. Experimental results and analysis

n n 1 ∑∑

(16)

f˜ is the estimated value of image gray, a, b, c and d are linear

(15)

3.2.2. Noise evaluation method in the spectral domain Spatial–spectral decorrelation(SSDC) is used to evaluate the noise of real hyperspectral images in the spectral domain [27]. The core of SSDC is signal removal of high correlation by using multiple linear regression based on high correlation between the

MZ =

l m ∑ ∑

1 l×m

1

f (i, j, z )

(21)

1

The PSNR of the image is: RSN = 20 lg

Mk

(22)

σn

PSNR reflects the noise level in the hyperspectral images. The greater the PSNR, the smaller the noise of the hyperspectral image, which implies the improvement effect of noise reduction in the spectral domain. The denoising performance of the proposed algorithm is analyzed by the root mean square error(RMSE) of the spectral curve after removing the noise and the original spectral curve. The equation is given as follows: RMSE =

1 l×m

l m ∑ ∑

√

∑Zmax z

(fden,z − fori,z )2

i=1 j=1

Zmax

(23)

3.3. Simulated data experiments Two simulated hyperspectral images, Hyperspectral Digital Imagery Collection Experiment (HYDICE) image of Washington DC Mall and hyperspectral images of Pavia University scene, are used to verify the denoising performance of the proposed algorithm [29]. Two subimages of Washington DC Mall and Pavia University scene, whose sizes are respectively 256×256×191 and 256×256×103, are adopted. For the simulated data, the corrupting noise is i.i.d. Gaussian with zero mean and standard deviation σ ∈{10%, 20%, 30%, 40%}. Fig. 2 shows the denoising results of different denoising algorithms for the 60th bands of Washington DC Mall with σ = 20%. 3DFFT and NLM both have a poor denoising effect in the subjective equality. The proposed algorithm and BM4D can achieve significantly better denoising effects than those of the other three algorithms. When the proposed algorithm is compared to BM4D, superior performance is obtained, especially for the details in the images. Fig. 3 shows the denoising results of different denoising algorithms for the 50th bands of Pavia University scene with σ = 30% and the proposed algorithm achieves the best denoising performance. Fig. 4 shows the PSNR comparison of denoising performance of different algorithms band by band for Washington DC Mall with σ = 20% and Pavia University scene with σ = 30%. The proposed algorithm can achieve better

Xu P., Chen B., Xue L. et al. / ISA Transactions 92 (2019) 315–324

319

Table 1 The Results of mean PSNR of different denoising algorithms (dB) Data source

Different algorithms

Gaussian noise with standard deviation σ (%) 10

20

30

40

Washington DC Mall

3DFFT NLM BM3D BM4D The proposed algorithm

25.06 21.46 27.57 32.50 35.72

23.56 21.31 24.47 28.69 31.92

21.83 21.07 23.00 26.65 29.49

20.20 20.75 21.99 25.33 27.85

Pavia University scene

3DFFT NLM BM3D BM4D The proposed algorithm

28.04 24.77 29.82 34.88 35.95

25.44 24.45 26.74 30.92 33.03

23.01 23.96 25.31 28.92 30.98

20.98 23.37 24.22 27.69 29.67

Table 2 Time comparison of different denoising algorithms.

Table 3 The mean PSNR of LMLSD for different denoising algorithms.

Data source

Different algorithms

Time consumption (s)

Different algorithms

Mean PSNR of LMLSD (dB)

Washington DC Mall

3DFFT NLM BM3D BM4D The proposed algorithm

2.79 4331.30 46.74 330.34 480.57 4.71 7568.47 105.31 627.78 641.48

25.03 31.38 36.51 35.71 39.85 40.38

Pavia University scene

3DFFT NLM BM3D BM4D The proposed algorithm

Original data 3DFFT NLM BM3D BM4D The proposed algorithm

PSNR than that of the other algorithms band by band for both the two different data source. Table 1 shows the mean PSNR comparison of two different data sources for different denoising algorithms with different values of σ . For both the Washington DC Mall and Pavia University scene with different values of σ , the proposed algorithm can achieve the highest mean PSNR in all denoising algorithms. For Washington DC Mall, in the case of σ from 10% to 40%, the proposed algorithm obtains 3.22 dB, 3.23 dB, 2.84 dB and 2.52 dB higher PSNR than that of the other algorithms, respectively. For Pavia University scene, in the case of σ from 10% to 40%, the proposed algorithm obtains 1.07 dB, 2.11 dB, 2.05 dB and 1.98 dB higher PSNR than that of the other algorithms, respectively. In this paper, time consumption is used to evaluate the computation complexity of different algorithms. Table 2 shows the time comparison of different denoising algorithms for Washington DC Mall and Pavia University scene. 3DFFT takes the shortest running time with the worst denoising performance. For different algorithms, less band count means less time consumption, so it takes less time for the Washington DC Mall than that for Pavia scenes. Combined with MNF and guide filtering, the proposed algorithm also shows higher computation complexity than that of BM4D. 3.4. Real data experiments The real data used in the experiment are the tea hyperspectral images. The real tea hyperspectral images are noise dominant within 380 nm–430 nm, so this range of spectra is discarded. The range of 430 nm–1023 nm is selected and a subimage with a size of 256 × 256 is chosen. The total is 469 slices and the gray level 12 bit unsigned integer. 3.4.1. Evaluation of the denoising effect in the spatial domain The tea hyperspectral images in 430 nm–530 nm and 930 nm– 1023 nm are severely affected by noise. Figs. 5–7 shows the denoising results of different denoising algorithms for bands at 435 nm, 840 nm, and 1015 nm wavelength.

The 3DFFT has a poor denoising effect in the spatial domain. NLM and BM3D have better denoising effects in the 2D image domain and enhances the edge of the image. However, for the band of 435 nm, the denoised image in the right half is poor because the local noise intensity in the spatial domain is not the same. BM4D utilizes the high inter-spectral and inter-spatial correlation of the hyperspectral images, and improves the spatial domain denoising effect greatly. The proposed algorithm not only makes full use of the high inter-spectral and inter-spatial correlation of the hyperspectral images and separates the denoise components, but also uses the guided image to improve the denoising performance. It overcomes the inconsistency of the local noise intensity in the spatial domain and generates the best denoising effect in the spatial domain Fig. 8 shows the LMLSD of all bands from 430 nm to 1023 nm wavelength for different denoising algorithms. As shown in Fig. 8, the proposed algorithm can achieve the best LMLSD performance. The proposed algorithm reduces the useless bands of hyperspectral images, overcomes the problem of inconsistent local noise intensity of tea hyperspectral images in the spatial domain, and further enhances the image denoising effect. The optimal band of BM4D is involved in the proposed algorithm as guided filter image, which can be quite helpful for those bands with dramatically rising. Therefore, in the 680 nm–770 nm bands, the denoising effect has also greatly improved. Table 3 shows the values of mean PSNR of LMLSD for different denoising algorithms. The proposed algorithm can achieve 0.55 dB, 4.67 dB, 3.84 dB, 9.0 dB, and 15.35 dB higher mean PSNR of LMLSD than that of BM4D, BM3D, NLM, 3DFFT, and the original data, respectively. Therefore, the proposed algorithm can achieve the best performance in the spatial domain. This part discusses the impact of three main parameters of hard-threshold λ4D , radius r and regularization ϵ of the proposed algorithm on the results. Table 4 shows the values of mean PSNR of the proposed algorithm for different values of hard-threshold λ4D , with radius r and regularization ϵ set as the default values of 2 and 0.042 , respectively. As the value of the hard-threshold value λ4D increases, PSNR value tends to decrease. When the value of λ4D is less than 1.2, the value of mean PSNR is almost kept the same. Meanwhile, the change of λ4D value has no significant effect on the PSNR value. In the following experiments, λ4D is set as the default value of 2.7. Table 5 shows that larger value of radius r

320

Xu P., Chen B., Xue L. et al. / ISA Transactions 92 (2019) 315–324

Fig. 2. Comparison of denoising performance for Washington DC Mall at the 60th band with σ = 20%.

Fig. 3. Comparison of denoising performance for Pavia University scene at the 50th band with σ of 30%.

of the proposed algorithm leads to lower PSNR value when ϵ is set as 0.0042 . Table 6 gives the mean PSNR for different values of ϵ when r is set as 2. It also shows that larger value of ϵ leads to lower value of mean PSNR. When ϵ is less than or equal to 0.0012 , the value of PSNR is kept the same. 3.4.2. Evaluation of the denoising effect in the spectral domain The experimental results of denoised spectral curves at f (85,130, z), f (85,170, z) and f (150,150, z) of the tea hyperspectral images by different methods are given in Figs. 9–11. Figs. 9–11 shows that the 3DFFT, NLM and BM3D have poor denoising performance in the 430 nm–550 nm and the 950 nm– 1023 nm, and especially in the 430 nm–470 nm there appears violent vibration. The BM4D takes the high correlation between the

spatial and the spectral domains into consideration and improves the overall denoising effect of the spectral domain. However, due to the low inter-spectral correlation in the 680 nm–770 nm, the denoising effect of BM4D for the hyperspectral images drops. The proposed algorithm firstly reduces the useless bands of hyperspectral images, and then uses guided filtering to recover details. Therefore, the proposed algorithm can achieve a better denoising effect for 680 nm–770 nm than BM4D. Fig. 12 shows that the proposed algorithm can achieve a better SSDC performance than that of the other algorithms at the different wavelengths. Table 7 shows the mean PSNR of SSDC for different denoising algorithms. The proposed algorithm can achieve 4.3 dB, 27.72 dB, 24.35 dB, 32 dB and 46.56 dB higher

Xu P., Chen B., Xue L. et al. / ISA Transactions 92 (2019) 315–324

Fig. 4. PSNR comparison of denoising performance of different algorithms band by band.

Fig. 5. Comparison of denoising performance of different algorithms at 430 nm wavelength.

Fig. 6. Comparison of denoising performance of different algorithms at 840 nm wavelength.

321

322

Xu P., Chen B., Xue L. et al. / ISA Transactions 92 (2019) 315–324

Fig. 7. Comparison of denoising performance of different algorithms at 1023 nm wavelength. Table 4 The mean PSNR for hard-threshold parameter λ4D .

Fig. 8. Comparison of LMLSD noise evaluation of different denoising algorithms.

λ4D

Mean PSNR (dB)

0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0 3.3 3.6 3.9 4.2

29.00 29.00 28.99 28.98 28.96 28.93 28.90 28.86 28.84 28.81 28.80 28.79 28.78 28.77

Table 5 The mean PSNR for parameter r.

Fig. 9. Spectral curves at f(85,130,z).

Fig. 10. Spectral curves at f(85,170,z).

r

Mean PSNR (dB)

2 4 6 8 10 12 14 16

28.84 28.16 27.44 26.70 26.00 25.32 24.66 24.03

Table 6 The mean PSNR for parameter ϵ .

ϵ

Mean PSNR (dB)

0.000012 0.000052 0.00012 0.00052 0.0012 0.0052 0.012 0.052 0.12 0.52

29.006 29.006 29.006 29.006 29.006 28.998 28.987 28.916 28.882 28.831

Xu P., Chen B., Xue L. et al. / ISA Transactions 92 (2019) 315–324

323

Table 8 Time comparison of different denoising algorithms. Different algorithms

Time consumption (s)

3DFFT NLM BM3D BM4D The proposed algorithm

11.72 19 021.37 415.38 1511.70 1655.85

proposed algorithm shows higher computation complexity than that of BM4D. Fig. 11. Spectral curves at f(150,150,z).

4. Conclusions

Fig. 12. Comparison of SSDC noise evaluation of different denoising algorithms. Table 7 The mean PSNR of SSDC for different denoising algorithms. Different algorithms

PSNR of SSDC (dB)

Original data 3DFFT NLM BM3D BM4D The proposed algorithm

24.13 38.39 46.04 42.67 66.09 70.39

PSNR of SSDC than that of BM4D, BM3D, NLM, 3DFFT, and original data, respectively. For NLM, 3DFFT and BM3D, failure in consider the high inter-spectral correlation results in poor spectral denoising performance. Compared with the BM3D, the BM4D algorithm matches 3D image blocks in 3D domain that achieves average 23.42 dB higher SSDC than that of BM3D in the spectral domain. Due to the low inter-spectral correlation in the 680 nm– 770 nm, the SSDC of BM4D decreases dramatically. The proposed algorithm firstly reduces the useless bands of hyperspectral images, and then uses guided filtering technology to recover the hyperspectral data in the 680 nm–770 nm, which can improve the denoising performance effectively. By introducing the MNF and guided image filtering, the proposed algorithm can also avoid the abrupt decrease of PSNR of SSDC for BM4D at the wavelength of around 450 nm. Therefore, the proposed algorithm can achieve the best performance in the spectral domain. 3.4.3. Evaluation of the computation complexity Table 8 shows the time comparison of different denoising algorithms. The time comparison result of the real tea hyperspectral images is similar to that of the simulated data. Since band count of real tea hyperspectral images is larger than that of both the simulated data, Washington DC Mall and Pavia University scene, it takes more time consumption for different algorithms. 3DFFT also takes the shortest running time with the worst denoising performance. Combined with MNF and guide filtering, the

In this paper, an improved algorithm for BM4D based on MNF and guided filtering is proposed. BM4D is a state-of-the-art denoising method for hyperspectral images and has been regarded as a well-known benchmark in this research field. Benefiting from MNF and guide image filtering technology, the proposed algorithm can blend the MNF and guide image filtering into BM4D to improve the denoising performance. With MNF set before the BM4D, the main component of the input hyperspectral images can be extracted from the noising component preliminarily. After denoising by BM4D, the guided image filtering is introduced to further improve the denoising effect. The change of hardthreshold value λ4D the proposed algorithm has no significant effect on the PSNR value. The parameters r and ϵ of the proposed algorithm both show that larger values of those parameters lead to lower PSNR value, so relatively small values are chosen for these two parameters in the experiments. According to the experimental results of the simulated data of Washington DC Mall and Pavia University scene, for the zero-mean Gaussian noise with different standard deviation, the proposed algorithm shows the best denoising performance. For the real tea hyperspectral images, the proposed algorithm can not only remove the spatial noise but also suppress the strong spectral noise more effectively than those of BM4D. Therefore, the proposed algorithm can be considered as a promising technique to denoise hyperspectral images. Acknowledgments The authors would like to thank Editor, Associate Editor and the anonymous reviewers for their much time and constructive comments to review and improve this paper. Funding This project was funded by the State Scholarship Fund of China Scholarship Council under Grant No. 201708330395, the Joint Funds of National Natural Science Foundation of China under Grant No. U1609218, the National Key Foundation for Exploring Scientific Instrument of China under Grant No. 61427808, the National Nature Science Foundation of China under Grants Nos. 41671415 and 61205200, and Zhejiang public welfare Technology Application Research Project of China under Grants No. 2016C32087. Conflict of interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

324

Xu P., Chen B., Xue L. et al. / ISA Transactions 92 (2019) 315–324

References [1] Landgrebe D. Hyperspectral image data analysis. IEEE Signal Process Mag 2002;19(1):17–28. [2] Zhang B. Advancement of hyperspectral image processing and information extraction. Int J Remote Sens 2016;20(5):1062–90. [3] Jiang Y. Research on regularization methods for improving spatial resolution of optical remote sensing images. Wuhan University; 2015. [4] Chen G, Qian S. Denoising and dimensionality reduction of hyperspectral imagery using wavelet packets, neighbor shrinking and principal component analysis. Int J Remote Sens 2009;30(18):4889–95. [5] Bourguignon S, Mary D, Slezak É. Sparsity-based denoising of hyperspectral astrophysical data with colored noise. In: Application to the MUSE instrument: Hyperspectral Image and Signal Processing: Evolution in Remote Sensing. 2010. [6] Vaiphasa C. Consideration of smoothing techniques for hyperspectral remote sensing. ISPRS J Photogram Remote Sens 2006;60(2):91–9. [7] Yang Z, Wang Y, Pan Z. Fluorescence spectrum denoising method for low concentration petroleum pollutants based on EMD-LWT. Acta Opt Sin 2016;(5):290–6. [8] Chen C, Lu Q, Peng Z. Preprocessing methods of near-infrared spectrun based on NLMS adaptive filtering. Acta Opt Sin 2012;32(5):286–91. [9] Stephan K, Hibbitts CA, Hoffmann H, et al. Reduction of instrumentdependent noise in hyperspectral image data using the principal component analysis: Applications to galileo NIMS data. Planet Space Sci 2008;56(3–4):406–19. [10] Zu Q, Zhang S, Cao Y, et al. Research on identification of cabbages and weeds combining spectral imaging technology and SAM taxonnmy. Spectrosc Spectr Anal 2015;(2):479–85. [11] Atkinson I, Kamalabadi F, Jones DL. Wavelet-based hyperspectral image estimation. In: 2003 IEEE international geoscience and remote sensing symposium, Vol. 2. 2003, p. 743–5. [12] Othman H, Qian SE. Noise reduction of hyperspectral imagery using hybrid spatial-spectral derivative-domain wavelet shrinkage. IEEE Trans Geosci Remote 2006;44(2):397–408. [13] Huo L, Feng X. Denoising of hyperspectral remote sensing image based on principal component analysis and dictionary learning. J Electron Inf Technol 2014;(11):2723–9. [14] Chen S, Hu X, Peng S. Hyperspectral imagery denoising using a spectralspatial domain mixing prior. J Comput Sci Tech-Ch 2012;27(4):851–61. [15] Yuan Q, Zhang L, Shen H. Hyperspectral imagery denoising employing a spectral-spatial adaptive total variation model. IEEE Trans Geosci Remote 2012;50(10):3660–77. [16] Kumar A, Ahmad MO, Swamy MNS. Image denoising via overlapping group sparsity using orthogonal moments as similarity measure. ISA Trans 2018;10:1–12. [17] Buades A, Coll B, Morel JM. Nonlocal image and movie denoising. Int J Comput Vis 2008;76(2):123–39. [18] Dabov K, Foi A, Katkovnik V, et al. Image denoising by sparse 3D transform-domain collaborative filtering. IEEE Trans Image Process 2007;16(8):2080–95. [19] Maggioni M, Katkovnik V, Egiazarian K, et al. Nonlocal transform-domain filter for volumetric data denoising and reconstruction. IEEE Trans Image Process 2013;22(1):119. [20] Chen G, Bui TD, Quach KG, et al. Denoising hyperspectral imagery using principal component analysis and block-matching 4D filtering. Can J Remote Sens 2014;40(1):60–6. [21] Maggioni M, Foi A. Nonlocal transform-domain denoising of volumetric data with groupwise adaptive variance estimation. Proc. SPIE Electron Imaging 2012;2:1–8. [22] He K, Sun J, Tang X. Guided image filtering. IEEE Trans Pattern Anal 2013;35(6):1397–409. [23] Luo GC, Chen GY, Tian L, et al. Minimum noise fraction versus principal component analysis as a preprocessing step for hyperspectral imagery denoising. Can J Remote Sens 2016;42:106–16. [24] Moore B. Principal component analysis in linear systems: Controllability, observability, and model reduction. IEEE Trans Automat Control 1981;26(1):17–32. [25] Green AA, Berman M, Switzer P, et al. A transformation for ordering multispectral data in terms of image quality with implications for noise removal. IEEE Trans Geosci Remote 1988;26(1):65–74. [26] Gao BC. An operational method for estimating signal to noise ratios from data acquired with imaging spectrometers. Remote Sens Environ 1993;43(1):23–33. [27] Gao L, Du Q, Zhang B, et al. A comparative study on linear regression-based noise estimation for hyperspectral imagery. IEEE J Stars 2013;6(2):488–98. [28] Jiang Q, Wang J. Study on signal-to-noise ratio estimation and compression method of operational modular imaging spectrometer multi-spectral images. Acta Opt Sin 2003. [29] http://lesun.weebly.com/hyperspectral-data-set.html.

Ping Xu was born in 1978. He received the Ph.D. degree in control theory and control engineering from Zhejiang university, Hangzhou, China, in 2006. He is currently an associate professor of College of Life Information Science & Instrument Engineering of Hangzhou Dianzi University, Hangzhou, China. His current research interests include compressive sensing, image processing and computer vision.

Bingqiang Chen received the B.E. degree in Measurement and control technology and instrument from Hangzhou Dianzi University, Hangzhou, China, in 2017. He is currently pursuing a M.Eng. degree in instrument science and technology at Hangzhou Dianzi University, Hangzhou, China. His current research interests include compressive sensing, tensor factorization, and machine vision technologies for crop sensing

Lingyun Xue received the B.Eng. degree in electronic precision machinery from Hangzhou Dianzi University, Hangzhou, China, in 1989, the M.Eng. degree in computer science and technology from Zhejiang University, Zhejiang, China, in 1999, and the Ph.D. degree in Biomedical Engineering from Zhejiang University, Zhejiang, China, in 2008. She is currently a professor in Hangzhou Dianzi University, Hangzhou, China. Her current research interests include detection technology and automatic equipment, pattern recognition and intelligent system. Jingcheng Zhang received the Ph.D. degree in agricultural remote sensing and information technology from Zhejiang University, Hangzhou, China, in 2012. He is currently an associate professor in Hangzhou Dianzi University, College of Life Information Science and Instrument Engineering, China. His current research interests include hypers Hangzhou, spectral remote sensing, spectral analysis on crop growing status, remotely sensed detection and monitoring of crop diseases and pests.

Lei Zhu received the B.Eng. degree and M.Eng. degree in automation from Liaoning Technology University, China, in 2001 and 2004, respectively, and the Ph.D. degree in control theory and control engineering from Zhejiang University, Hangzhou, China, in 2007. He was a visiting scholar at UMass Lowell in 2017. He is currently an associate professor in Hangzhou Dianzi University, Hangzhou, China. His current research interests include pattern recognition and data mining.

Hangbo Duan received the B.E. degree in Measurement and control technology and instrument from Hangzhou Dianzi University, Hangzhou, China, in 2018. His current research interests include compressive sensing and machine vision.