Despeckling of ultrasound images of bone fracture using M-band ridgelet transform

Optik 125 (2014) 1417–1422

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Despeckling of ultrasound images of bone fracture using M-band ridgelet transform Deep Gupta ∗ , R.S. Anand, Barjeev Tyagi Department of Electrical Engineering, Indian Institute of Technology Roorkee, Roorkee 247667, Uttarakhand, India

a r t i c l e

i n f o

Article history: Received 4 March 2013 Accepted 27 August 2013

Keywords: Ultrasound imaging Despeckling M-band ridgelet M-band wavelet

a b s t r a c t Ultrasound imaging is one of the most important and cheapest instrument of the medical imaging modalities. The quality of ultrasound imaging is degraded due to various types of noise and artifacts. Among these noise and artifacts, speckle is a main factor which degrades the quality and most importantly texture information present in ultrasound images. This paper presents a despeckling method based on M-band ridgelet transform which combines the M-band wavelet with ridgelet transform. The M-band ridgelet transform overcomes the limitations of the ordinary ridgelet transform by replacing the 2-band wavelet transform to analyze the edges and features present in the images. The performance of the proposed method is evaluated by conducting various experiments on both the ultrasound images of bone fracture and others also. Experiments show that the proposed method produces better results of removing the speckle and preserving the edges and image details as compared to the others. © 2013 Elsevier GmbH. All rights reserved.

1. Introduction Currently, the research in medical imaging has produced many different imaging modalities for the clinical purpose. The most common imaging modalities used in orthopedics are X-rays, computed tomography (CT), magnetic resonance imaging (MRI) and ultrasound. However, these medical imaging techniques use the ionizing radiation based on different energy sources such as internal, external and combination of both which raise important safety concerns for the human being [1]. Among different imaging modalities, ultrasound imaging has many advantages such as its cost effectiveness, portability, acceptability and safety. Different examinations of 243 apophyseal fractures in adolescents with X-rays and ultrasound imaging are reported [2], in which 80 cases were diagnosed by X-rays and 97 by ultrasound successfully. Hübner et al. described the possibility of the diagnosis for the fractures of the children using ultrasound imaging [3]. The authors have also suggested that the ultrasound assessment without radiography should be used in particular cases such as bulge fractures or mildly displaced, simple fractures of the long bones of the fore arm, humerus, femur, lower leg and clavicle. In [4], Rathfelder and Paar presented the experimental results of 2006 X-rays in which only 345 fractures were diagnosed completely. They proposed the possible application of ultrasonography and its good results on the

∗ Corresponding author. Tel.: +91 01332 286364; fax: +91 01332 273560. E-mail addresses: [email protected], [email protected] (D. Gupta), [email protected] (R.S. Anand), [email protected] (B. Tyagi). 0030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2013.08.007

same experiments. Heiner et al. demonstrated an effective method for rapid identification of long bone fractures [5]. In [6], a simulation model has been proposed also for the ultrasound diagnosis of bone fracture. Assessment of bone fracture using ultrasound imaging has an advantage of immediate clinical correlation and can be made by the people with minimal training in the use of ultrasound [2,7,8]. It has also found that ultrasound imaging was more sensitive than conventional radiography for rib fracture diagnosis [9–11]. However, the images obtained from ultrasound imaging are of relatively poor quality due to speckle considered as multiplicative noise. Speckle affects fast human interpretation as well as the accuracy of the computer assisted methods also. Furthermore, despeckling is of great need in ultrasound imaging and is considered as a challenging problem. Despeckling algorithms should be designed in such a manner that they suppress the speckle as much as possible without any significant loss of information. Noise suppression methods can be classified in two categories, viz. spatial domain and transform domain [12]. Currently lot of research works on image processing is concentrated in the transform domain. In that series, wavelet thresholding has been presented as a true signal estimation technique that utilizes the capabilities of wavelet transform (WT) for signal denoising [13]. However, the problem experienced is generally smoothening of edges. In [14], wavelet based total variation (WT-TV) method has been reported in which noisy image undergoes several iterations for suppressing the noise and leads to blurring effect. Wavelet based bilateral filtering (WT-BLF) approach provides better denoising and preserves the edges effectively [15]. This method utilizes the potential features of both wavelet thresholding and bilateral filter at the

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same time. However, the WT is optimal for representing a function with one dimensional, i.e. point singularities. However, it is less efficient in representing the sharp transition like line and curve singularities due to its limitation of direction. To overcome the limitation of the wavelets, the authors have reported the ridgelet representation of multidimensional signals which is used to map the line singularities to the point singularities using radon transform and after that the wavelet transform is used to provide better performance for characterizing the point singularities in radon transform [16]. In literature, ridgelet transform (RT) has been applied to various image processing applications, such as image denoising [16–18], feature extraction [19] and texture classification [20]. Ridgelet transform provides better results and breaks the limitation of the wavelets. However, two band wavelet transform must be performed in the radon domain to complete the ridgelet transform. It also derives another shortcoming of the standard wavelet. They are only capable to analyze low frequency signals but not for high frequency signals [21]. So in the presented work, M-band ridgelet transform is used for despeckling using Mband wavelet decomposition in radon domain. M-band wavelet decomposition helps also to enlarge the high frequency components. The rest of the paper is structured as follows. Section 2 presents the methodologies used to present an algorithm. Section 3 illustrates the implementation of the proposed method based on M-band ridgelet transform. To evaluate the performance of different methods, various experimental results are presented in Section 4. Conclusions are drawn in Section 5.



 RT (a, b, ) =

R2

RT (a, b, ) =

 ab (t)ı(x cos  + y sin  − t)dt dxdy (5)

s(x, y) R

ab (t)Ra (, t)dt R

So Ra (, t) is the radon transform of the signal s(x, y) which is as follows



Ra (, t) =

s(x, y)ı(x cos  + y sin  − t)dxdy

(6)

R2

The ridgelet transform is evaluated by applying the one dimensional wavelet transform to the slices of the radon transform. For a 2D signal, the Radon transform can be obtained with the fast Fourier transform (FFT). In [23], authors have reported the M-band ridgelet transform for texture classification in which 1D 2-band wavelet transform is replaced by the M-band wavelet transform along the radial and angular lines separably. The M-band wavelet transform is used to decompose the signal into M × M channels which are capable to enlarge the noisy subband. 2.2. À Trous algorithm (AT) À trous algorithm has been reported by Murtagh et al. [24]. This algorithm is used to decompose the data in different scales and obtain the low frequency part which has the same size as the original image. An image is decomposed as a superposition of the form

sAT (x, y) = snr (x, y) +

nr 

dk (x, y)

(7)

k=1

2. Methodology

A summary of the AT algorithm is as follows: 2.1. M-band ridgelet transform As proposed in [16], ridgelet transform has been applied in different image processing algorithm. Consider there is a univariate function : R → R which satisfy the admissibility condition as [22]



| ˆ ()|2 d < ∞ ||2

(1)

where ˆ denotes the Fourier transform of the univariate function  which has a vanishing mean (t)dt = 0. For each a > 0, b ∈ R and  ∈ [0, 2], the bivariate ridgelet ab : R2 → R2 is defined as [22,23]

 ab (x, y)

−1/2

=a

x cos  + y sin  − b a

 (2)

This function ab (x, y) has constant value along the lines x cos  + y sin  = K, where K is constant, a > 0 is scale parameter, b is the location scale parameter and  is an orientation parameter. For a given integrable bivariate signal s(x, y), ridgelet coefficients are defined as

1. Start with an image s(x, y) and initialize k to 0. 2. Evaluate the coarser approximation sk−1 (x, y) of the original image by computing a convolution of the data with the help of 2D low pass filter.

⎛

1 h= 256

1

4

6

4

1

⎞

⎜ 4 16 24 16 4 ⎟ ⎜ ⎟ ⎜ 6 24 36 24 6 ⎟ ⎜ ⎟ ⎝ 4 16 24 16 4 ⎠ 1

4

6

4

(8)

1

This filter is based on a B3 cubic spline interpolation, which leads to a iterative convolution with a template of 5 × 5. 3. Compute the difference between two consecutive approximations dk (x, y) = sk−1 (x, y) − sk (x, y)

(9)

4. Go to step 2, if k < nr where nr is the number of resolution for evaluating the approximations. 5. dk (x, y) includes the information of the two successive approximations dk (x, y) = {d0 (x, y), d1 (x, y), . . ., dnr (x, y)}

(10)



RT (a, b, ) =

s(x, y) R2

ab (x, y)dxdy

(3)

2.3. Thresholding

(4)

Various thresholding schemes are provided in the literature. The main task of thresholding approach is the proper selection of the threshold value (T). Now thresholding is concentrated on the neighborhood thresholding, called as NeighShrink (NS) also which has been improved further by Zhou and Cheng [25]. Several quantitative evaluations have been done and shown that NeighShrink performs better than other existing methods. The performance of

Due to

 ab (x, y)

=

ab (t)ı(x

cos  + y sin  − t)dt

R

where

ab (t)

= a−1/2 ((t − b)/a).

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the M-band ridgelet filtering algorithm is evaluated by despeckling of the high frequency coefficients using soft and NeighShrink thresholding algorithms. Soft thresholding is used to approximate RT (x, y) of the signal [13]. the noisy M-band ridgelet coefficients sM The coefficients whose absolute values are lower than the particular threshold (T) are first set to zero and then scaling the nonzero coefficients, i.e. whose values are greater than threshold (T). 2.3.1. NeighShrink thresholding To achieve the threshold coefficient, an improved NeighShrink (NS) algorithm is proposed that is based on the Stein’s unbiased risk RT (x, y) to estimate (SURE) [25]. For the M-band ridgelet coefficient sM be thresholded, consider a square window w(x, y) centered at the  2 coefficients is considered. Let S 2 (x, y) = sRT (k, l) and (k,l) ∈ w(x,y) M the thresholding expression is given as



RT sˆM (x, y)

=

T2 1− 2 S (x, y)



RT sM (x, y)

(11)

+

RT (x, y) sˆM

where is the estimator of the unknown noiseless coefficient and thresholding factor ∅ = (1 − T 2 /S 2 (x, y))+ . Here the ‘+’ sign means to keep only the positive values while it is set to zero when it is negative. The optimal value of the threshold (T) and window size l are determined for every subband using SURE by minimizing the mean squared error or risk of the corresponding subband. Stein showed that for almost any fixed estimator RT = s RT (x, y) based on the data sRT = sRT (x, y), the risk can be estiˆM sˆM M M mated as RT RT 2 RT E{||ˆsM − sM || } = E{SURE(sM , T, l)}

(12)

RT , T, l) = N + E{||G(sRT )||2 + 2∇ · G(sRT )} and G(r) = where SURE(sM M M n RT − sRT , n is the number of the M-band ridgelet {G(i)}i=1 = sˆM M coefficients in a subband. The optimal threshold T and neighborRT , T, l). ing window size l for different subband minimize SURE(sM Accordingly, RT (T, l) = arg min SURE(sM , T, l)

Fig. 1. Despeckling results for simulated speckled ultrasound image. (a) Original image. (b–d) Images degraded with the speckle noise of variance as 0.1, 0.2 and 0.3, respectively. (e–g) Output images processed with the proposed method.

(13)

all/abdomen.htm and http://www.ultrasoundcases.info/. The analysis has been performed on several ultrasound images of bone fracture and other images to evaluate the validity of the proposed method. These images were added with different levels of speckle noise controlled by varying the noise variance. To investigate the noise suppression and edge preservation performance of the proposed method, various performance indices are used such as mean squared error (MSE), peak signal to noise ratio (PSNR), structural similarity index metrics (SSIM), correlation coefficient (), universal image quality index (UQI) and Pratt’s figure of merit (FOM). The MSE and PSNR are used to measure the noise suppression capability of the despeckling approaches. Other parameters like UQI [26] and SSIM [27] have been also used to measure the closeness of the fine details in the filtered image with respect to the original image. The  [28] is used to measure how closely the approximated image resembles the original image. For the quantitative evaluation of the edge preservation in filtered image, Pratt’s figure of merit (FOM) [29] is most commonly used parameter in which a scalar multiplier ˛ = 1/9 is used for displaced edges from its original location.

3. Implementation steps

4.1. Results and discussions

For despeckling of ultrasound medical images and implementing the above aspects, the proposed algorithm is formulated as follows:

On the basis of results obtained, the denoising abilities of the present approach are presented/analyzed here qualitatively and quantitatively. For such purpose, four different types of experimentation have been performed. Observations on each of them as presented below.

1. Start with the speckled ultrasound image s(x, y) and apply the À trous algorithm with k = 3 scales. 2. Evaluate the radon transform on each detail subbands of k scale. 3. Apply M-band wavelet transform on the radon coefficients, to RT (x, y). Here, 3-band compute the M-band ridgelet coefficients sM wavelet transform is used to implement the above aspects. 4. After getting the coefficients from step (3), calculate the optimal value of the threshold corresponding to the minimize risk as per Eqs. (12) and (13). RT (x, y) 5. Apply the threshold on the M-band ridgelet coefficients sM obtained from the step (3), to compute the approximated or RT (x, y) using Eq. (11). threshold coefficients sˆM 6. Reconstruct the despeckled image sˆ(x, y) with the approximated coefficients, obtained from step (5). 4. Experimentation and analysis of results To evaluate the effectiveness of the proposed method, test ultrasound images were acquired from the open source medical image database available at http://rad.usuhs.edu/medpix/ parent.php3?Mode=image atlas, http://www.medison.ru/uzi/eng/

4.1.1. Experiment 1 To investigate the performance of the proposed method, 60 different medical ultrasound images are used. To perform the experiment, ultrasound images added with the speckle noise of different variance as 0.1, 0.2 and 0.3 are shown in Figs. 1(b)–(d). Denoised images are shown in Figs. 1(e)–(g) which show the noise suppression as well as visualization capability of the proposed method. Apart from the visual assessment, the performance has been extensively analyzed and evaluated using different performance measures as mentioned above. The qualitative performance of the proposed method is shown in Fig. 2. In Fig. 2, the MSE and PSNR values show noise suppression ability of the proposed method while edge preservation quality is illustrated by the higher value of FOM, i.e. closer to unity. From Fig. 2, it can be seen that the FOM gets an approx value of 0.8, which signifies retention of large amounts of edges for all ultrasound images. The UQI varies approx between 0.7 and 0.9, which represents less distortion between the original and processed image. The values of  approach to 1, which insures a

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Fig. 4. Ultrasound image of rib fracture with cortical interruption.

Fig. 2. Comparison between the performance of the proposed method in terms of noise suppression, feature and edge preservation.

strong correlation between the original and reconstructed image. It is observed also from Fig. 2 that the SSIM gets the value approx to 0.9, which indicates that the performance of the proposed method is producing more detailed images in which most of the structural features are preserved. 4.1.2. Experiment 2 To compare the despeckling ability of the proposed method, some other remarkable methods are used. To perform the comparative evaluation, different ultrasound images are used in which one of them is shown in Fig. 3(a). Firstly, wiener filter is used on the wavelet coefficients of a speckled image. The output image processed with wiener filter using wavelet transform (WT-wiener) is shown in Fig. 3(b). The result of the proposed method is compared also with the much efficient wavelet based NeighShrink thresholding (WT-NS) and WT-NS using bilateral filter (WT-NS-BLF). The output image processed with WT-NS and WT-NS-BLF methods are shown in Figs. 3(c) and (d), respectively. Fig. 3(e) shows the result of WT-TV, which also removes the noise by minimizing the norm of an image calculated with the noise statistics. Finally, the comparison is made between the ridgelet transform with NeighShrink (RT-NS) and proposed algorithm using M-band ridgelet transform. The outcomes of both methods are shown in Figs. 3(f) and (g).

Fig. 3. Despeckling results for displayed ultrasound image. (a) Speckled ultrasound image. Results processed with (b) WT-wiener, (c) WT-NS, (d) WT-NS-BLF, (e) WTTV, (f) RT-NS, (g) proposed method. (h) Line profile across the image. Result of line profile processed with (i) WT-wiener, (j) WT-NS, (k) WT-NS-BLF, (l) WT-TV, (m) RT-NS, (n) proposed method.

Fig. 5. Ultrasound image of comminuted fibula fracture with cortical interruption.

Another comparative analysis is done also based on line profile which indicates the gray level intensities across a predefined line in the ultrasound image shown in Fig. 3(a), for further analysis. The line profile along the line in the speckled image is shown in Fig. 3(h). Figs. 3(i)–(n) show the different line profiles along the same line across the test ultrasound image processed with WTwiener, WT-NS, WT-NS-BLF, WT-TV, RT-NS and proposed method, respectively. It is observed from line profile analysis, shown in Fig. 3 that the contents of the image are well preserved and the transitions of despeckled images are smoother than noisy image. 4.1.3. Experiment 3 To evaluate the superiority of the proposed method, another dataset of thirty different bone fracture ultrasound images is used. These images are used for enhancement purpose by suppressing the speckle from the original bone fracture ultrasound images. Moreover, we compared the enhancing capability of the proposed method with WT-TV and RT-NS method, considering the noise suppression capability as mentioned above. Figs. 4 and 5 show the enhancement of ultrasound images of rib and fibula fracture with cortical interruption, respectively. The despeckled fracture ultrasound images processed with WT-TV, RT-NS and proposed method are shown in Figs. 4(b)–(d) and 5(b)–(d), respectively. From the analysis of visual results, it is observed that the processed images with the proposed method give a better visual appearance in comparison to others with smooth boundaries and enhanced the texture contrast. Subjective outcomes of the proposed method are supported by different objective assessment parameters. Table 1 shows the comparative evaluation of four different methods based on the values of different objective indices. From Table 1, it is observed that the proposed method provides higher PSNR values as compared to others. The average values of the UQI, SSIM and FOM are 0.764, 0.8613 and 0.77345 for WT-NS method, respectively which are increased up to 0.9149, 0.9751 and 0.837 for the proposed method. The averaged value of the correlation coefficients is 0.99055 for the proposed method which shows an improvement in comparison to 0.96553 of WT-NS, 0.96569 of WT-TV and 0.98334 of RT-NS method. Finally from Table 1, it is concluded that all the assessment parameters used to evaluate the quality and edge preservation ability of the proposed method have the largest values in case of bone fracture ultrasound image enhancement. 4.1.4. Experiment 4 To analyze the robustness of the proposed method, four standard test images shown in Fig. 6 have been used. All these images are initially corrupted with the simulated speckle noise with different variance and later despeckled using the proposed method and others considering their despeckling capability. Figs. 7(a)–(f) show the box plots for comparative analysis between

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Table 1 Performance comparison of despeckling methods. Bone fracture US images

Despeckling methods

Assessment parameters

PSNR

UQI



SSIM

FOM

#1

WT-NS WT-TV RT-NS Proposed

33.85 33.24 36.85 37.62

0.8092 0.8432 0.8532 0.9103

0.97532 0.97595 0.98821 0.99126

0.9166 0.9248 0.9477 0.9766

0.8293 0.7843 0.8423 0.8452

#2

WT-NS WT-TV RT-NS Proposed

30.15 31.14 33.17 35.63

0.7187 0.8255 0.8038 0.9195

0.95575 0.95543 0.97847 0.98985

0.8097 0.8731 0.8638 0.9736

0.7176 0.7464 0.7953 0.8288

Fig. 6. Images used for despeckling in experimentation. (a) Lena. (b) Boat. (c) Pirate. (d) Butterfly.

• Fig. 7(c) ensures the strong correlation between the original and the despeckled images with approx 2% and 1.48% higher value of  over WT-TV and RT-NS method, respectively. • Figs. 7(d) and (e) indicate exhaustive comparison of the proposed method with others in terms of quality evaluation. The proposed method gains approx 9% and 4–5% larger SSIM value than WT-TV and RT-NS method. • From Fig. 7(f), it is observed that the proposed method has not only the highest (approx 5–11% higher) FOM value but it has the value closer to unity also which means the features and edges are well preserved using the proposed method. 5. Conclusion In this paper, M-band ridgelet transform with the improved NeighShrink approach has been presented to suppress the speckles from the bone fracture ultrasound images. The M-band ridgelet transform based despeckling method exploits the features of the Mband wavelet transform in place of 2-band wavelet transform. This method utilizes the variation of frequency resolution features of À trous approach by which a speckled image has been decomposed into different scales. NeighShrink provides the modified threshold coefficients which improve the despeckling efficiency also. Experiments were carried out on different ultrasound and natural images with different noise levels to do subjective evaluations. Experiments also have been performed for enhancement of bone fracture ultrasound images by smoothing the homogeneous area as well as preserving the important features. From the experimental results, it is observed that the proposed method not only shows better visual appearance of the enhanced regions of the ultrasound images, but also exhibits the improved performance in terms of different quantitative measures.

Fig. 7. Comparative performance analysis of proposed method (M3) with WT-TV (M1) and RT-NS (M2) in terms of (a) MSE, (b) PSNR, (c) , (d) UQI, (e) SSIM, (f) FOM.

the performance of the proposed method and the others. In each box plot, the top and bottom of each rectangular box indicate the 25th and 75th percentile, respectively, with the median shown inside the box. From the Figs. 7(a) and (b), it is clearly seen that the median values of the MSE and PSNR are lowest and highest, respectively for the proposed method. This indicates the superiority of the proposed method over others in terms of noise suppression. From the analysis of all performance indices values, it can be summarized that • The proposed method obviously outperforms the WT-TV. In addition, proposed method gains 5–17% greater value (in dB) of PSNR than the WT-TV method. • The proposed method provides relatively stable (approx 3–6% larger value) PSNR gains over ordinary ridgelet based approach.

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