Despeckling of ultrasound images

Transcription

1 Despeckling of ultrasound images Gunjan Guru Nanak Dev Engineering College, Ludhiana Abstract In medical image processing, image denoising has become a very essential exercise all through the diagnose. Negotiation between the preservation of useful diagnostic information and noise suppression must be treasured in medical images. In ultrasound images, a special type of acoustic noise, technically known as speckle noise, can restrain information which is valuable for the general practitioner. It is the major factor of image quality degradation. Many denoising techniques have been proposed for effective suppression of speckle noise. Speckle has been treated as a distracting artefact as it tends to degrade the resolution and the object detectability. Moreover, in US images, the speckle noise has a spatial correlation length on each axis, which is the same as resolution cell size. This spatial correlation makes the speckle suppression a very difficult and delicate task, hence, a trade-off has to be made between the degree of speckle suppression and feature preservation. In this paper, a wavelet domain method for noise filtering in ultrasound images is proposed. The proposed algorithm exploits generally valid knowledge about the correlation of significant image features across the resolution scales to perform a preliminary coefficient classification. This preliminary coefficient classification is used to empirically estimate the statistical distributions of the coefficients that represent useful image features on the one hand and mainly noise on the other. The adaptation to the spatial context in the image is achieved by using a wavelet domain indicator of the local spatial activity. The results demonstrate its usefulness for noise suppression in ultrasound images. Keywords Despeckling, Generalized likelihood ratio, noise reduction, wavelets. 1. INTRODUCTION Speckle noise is a granular noise that inherently exists in and degrades the quality of the ultrasound images. Speckle noise is a phenomenon that accompanies all coherent imaging modalities in which images are produced by interfering echoes of a transmitted waveform [16]. Ultrasound is an imaging technique which is based on recording of phase and amplitude of reflected ultrasound wave. In ultrasound images, speckle noise suppression is a particularly delicate and difficult task. A trade-off between noise reduction and the preservation of actual image features has to be made in a way that enhances the diagnostically relevant image content. Image processing specialists usually lack the biomedical expertise to judge the diagnostic relevance of the despeckling results. For example, in ultrasound images, speckle noise may contain information useful to medical experts. This motivates the construction of robust and versatile denoising methods. In this paper, one robust method is proposed that employ a preliminary detection of the wavelet coefficients that represent the features of interest in order to empirically estimate the conditional pdf s of the coefficients given the useful features and given background noise. At the same time, the preliminary coefficient classification is also exploited to empirically estimate the corresponding conditional pdf s of the local spatial activity indicator. The classification step of the proposed method involves an adjustable parameter that is related to the notion of the expert defined relevant image features. In certain applications the optimal value of this parameter can be selected as the one that maximizes the signal-to-noise ratio (SNR).However in most medical applications the tuning of this parameter leading to gradual noise suppression may be advantageous. The proposed algorithm is simple to implement and fast. We demonstrate its usefulness for despeckling and enhancement of the ultrasound images. 2. SPECKLE NOISE IN ULTRASOUND IMAGES It is an ultrasound-based diagnostic medical imaging technique used to visualize muscles and many internal organs, their size, structure and any pathological injuries with real time tomographic images. Obstetric sonography is commonly used during pregnancy. It is one of the most widely used diagnostic tools in modern medicine. The technology is relatively inexpensive and portable, especially when compared with other imaging techniques such as magnetic resonance imaging (MRI) and computed tomography (CT). It has no known long-term side effects and rarely causes any discomfort to the patient. Since it does not use ionizing radiation, ultrasound yields no risks to the patient. It provides live images, where the operator can select the most useful section for diagnosing thus facilitating quick diagnoses. The proposed work aims to suppress speckle in ultrasound images. Speckle noise affects all coherent imaging systems including medical ultrasound. Within each resolution cell a number of elementary scatterers reflect the incident wave towards the sensor. The backscattered coherent waves with different phases undergo a constructive or a destructive interference in a random manner. The acquired image is thus corrupted by a random granular pattern, called speckle that delays the interpretation of the image content. A speckled image is commonly modeled as v 1 = f 1 υ: where f={f 1,f 2,f 3,.. f n } is a noise-free ideal image, V={ v 1,v 2, v 3...v n }speckle noise and υ = {υ 1,υ 2,υ 3,.υ n } is a unit mean random field[21]. Volume 1, Issue 2, July 2013 Page 29

2 In the medical literature, speckle noise is referred as texture and may possibly contain useful diagnostic information. The desired grade of speckle smoothing preferably depends on the specialist s knowledge and on the application. For automatic segmentation, sustaining the sharpness of the boundaries between different image regions is usually preferred while smooth out the speckled texture. For visual interpretation, smoothing the texture may be less desirable. Physicians generally have a preference of the original noisy images more willingly than the smoothed versions because the filters even if they are more sophisticated can destroy some relevant image details. Thus it is essential to develop noise filters which can secure the conservation of those features that are of interest to the physician. The wavelet transform has recently entered the field of image denoising and it has firmly recognized its stand as a dominant denoising tool. 3. WAVELET DOMAIN NOISE FILTERING Recently there has been significant investigations in medical imaging area using the wavelet transform as a tool for improving medical images from noisy data. Wavelet denoising attempts to remove the noise present in the signal while preserving the signal characteristics, regardless of its frequency content. As the discrete wavelet transform (DWT) corresponds to basis decomposition, it provides a non-redundant and unique representation of the signal. Several properties of the wavelet transform, which make this representation attractive for denoising, are:- Multiresolution - image details of different sizes are analyzed at the appropriate resolution scales. Sparsity - the majority of the wavelet coefficients are small in magnitude. Edge detection - large wavelet coefficients coincide with image edges. Edge clustering - the edge coefficients within each sub band tend to form spatially connected clusters. During a two level of decomposition of an image using a scalar wavelet, the two-dimensional data is replaced with four blocks. These blocks correspond to the sub bands that represent either low pass filtering or high pass filtering in each direction. The procedure for wavelet decomposition consists of consecutive operations on rows and columns of the twodimensional data. The wavelet transform first performs one step of the transform on all rows. This process yields a matrix where the left side contains down sampled low pass coefficients of each row, and the right side contains the high pass coefficients. Next, one step of decomposition is applied to all columns; this results in four types of coefficients, HH, HL, LH and LL. 4. MEDICAL ULTRASONOGRAPHY Ultrasonography is considered to be one of the most powerful techniques for imaging organs and soft tissue structures in the human body. It is often preferred over other medical imaging methods because it is non-invasive, portable, versatile, and it does not use ionizing radiations. In physics, the term ultrasound applies to all sound waves with a frequency above the audible range of human hearing, about 20,000 Hz. The frequencies used in diagnostic ultrasound are typically between 2 and 18 MHz [22]. In diagnostic ultrasonography, the ultrasonic waves are produced by electrically stimulated a piezoelectric crystal called transducer. As the beam strikes an interface or boundary between tissues, some of the sound waves are reflected back to the transducer as echoes. The echoes are then converted into electrical impulses that are displayed on an oscilloscope, presenting a picture of the tissues under examination.several different modes of ultrasound are used in medical imaging. These are: a) A-mode: A-mode is the simplest type of ultrasound. A single transducer scans a line through the body with the echoes plotted on screen as a function of depth. Therapeutic ultrasound aimed at a specific tumour or calculus is also A- mode, to allow for pinpoint accurate focus of the destructive wave energy. b) B-mode: In B-mode ultrasound, a linear array of transducers simultaneously scans a plane through the body that can be viewed as a two-dimensional image on screen. c) M-mode: M stands for motion. Ultrasound pulses are emitted in quick succession each time, either an A-mode or B- mode image is taken. Over time, this is analogous to recording a video in ultrasound. As the organ boundaries that produce reflections move relative to the probe, this can be used to determine the velocity of specific organ structures. d) Doppler mode: This mode makes use of the Doppler Effect in measuring and visualizing blood flow. It works on principle of change in frequency of the investigating beam caused by a moving target. 5. PROPOSED METHOD The idea behind the proposed algorithm is to empirically estimate the probabilities and the probability density functions. Let N denote the number of wavelet coefficients in a detail image. For each detail image w j D ={w 1,j D,..w N,j D }, we first estimate the mask x j D = {x 1,j D,..x N,j D }, which indicates the positions of significant wavelet coefficients (representing the signal of interest). For estimating the mask the following equation (1) is used: x D k,j = 0, if w D k,j y D k,j+1 < (K σ D j) 2 (1) Volume 1, Issue 2, July 2013 Page 30

3 1, if w D k,j y D k,j+1 (K σ D j) 2 where K is a heuristic, tunable parameter that controls the notion of the signal of interest and σ D j is an estimate of the noise standard deviation which is computed using an enhanced equation (2): σ D j = [median (median (abs(x-med)* 4))/0.6745] (2) where med= median(median(x)) and X=std2(X). Noisy Detail Image Detected mask Figure.1. Examples of the empirical pdf s and fitted log-ratios in the proposed method, for the top left ultrasound image. In estimating σ D j, each sub band the constant is calculated from the filter coefficients of the high pass filter g and the low pass filter h of the discrete wavelet transform. Now compute the local spatial activity indicator e k by averaging the magnitude of the eight neighbouring coefficients in a square window at the same scale. Let X k denote a random variable, which takes values x k from the binary label set (0, 1). The hypothesis the wavelet coefficient w k represents a signal of interest is equivalent to the event X k =1, and the opposite hypothesis is equivalent to X k = 0. The wavelet coefficients representing the signal of interest in a given sub band are identically distributed random variables with the probability density function p Wk Xk (w k 1). Similarly, the coefficients in the same sub band, corresponding to the absence of the signal of interest, are random variables with the probability density function p Wk Xk (w k 0). Having the estimated mask x={x 1.xN }, let S o = {k: x k = 0} and S 1 = {k: x k = 1}. The empirical estimates p M k /X k (m k 0) and p E k /X k (e k 0) are computed from the histograms of {m k : k Є S o } and {e k :k Є S o } respectively (by normalizing the area under the histogram). Similarly, p M k /X k (w k 1) and p E k /X k (e k 1) are computed from the corresponding histograms for k Є S 1. This estimation approach still requires the probability ratio. Reasoning that P (X k =1) can be estimated as the fractional number of labels for which x k =1, now estimate the parameter r as given in equation (3): N N r= Σ k=1 x k / N- Σ k=1 (3) Now estimate each wavelet coefficient as stated in equation (4): where y x =(rξ k η k /1+ rξ k η k )w k (4) ξ k= p M k /X k (m k 1)/ p M k /X k (m k 0) and η k = p E k /X k (e k 1)/ p E k /X k (e k 0) (5) Volume 1, Issue 2, July 2013 Page 31

4 In Fig. 1, we show an example of the empirical densities and p M k /X k (m k x k ) and p E k /X k (e k x k ). The direct computation of the ratios ξ k and η k from the normalized histograms shown in Fig. 1 is not appropriate due to errors in the tails. One solution is to first fit a certain distribution to the histogram. Here, now apply a simpler approach, observing that both log(ξ k ) and log(η k ) can be approximated well by fitting a piece-wise linear curve as illustrated in Fig. 1 using the following equations: log(ξ k ) = a1+b1m k, ξ k <1 a2+b2m k, ξ k >=1 (6). log(η k ) = c1+d1e k, η k <1 c2+d2e k, η k >=1 (7) The proposed algorithm consists of the following steps: Step 1: Take the input image ( jpg, tif ). Step 2: Add speckle noise in the original speckle free image. Step 3: Perform the DWT of the noisy image up to 4 levels (J=4) to obtain several sub bands. Step 4: Estimate the noise standard deviations σ D j for each sub band using an enhanced equation (2). Step 5: For each scale 2 j, j=1 J-1 a) Now estimate the mask x D j using equation (1). b) Compute the local spatial activity indicator e k, by averaging the magnitude of the eight neighbouring coefficients in a square window at the same scale. Step 6: Calculate probability ratio r using equation (3). Step7: Define S 0 = {k : x k = 0} and S 1 = {k : x k = 1} and estimate p M X (m 0), p M X (m 1),p E X (e 0) and p E X (e 1), from the corresponding histograms. Step 8: Now estimate each wavelet coefficient using equation (4). Step 9: Fit the log-ratios log (ξ k ) and log (η k ) from equation (6) and (7). Step 10: Perform the inverse DWT to reconstruct the denoised image. Figure 2. Gradual noise suppression in ultrasound images using the proposed method. Volume 1, Issue 2, July 2013 Page 32

5 Figure 3: Visual comparison of result of various despeckling techniques with proposed technique for liver.jpg. Figure 4: Visual comparison of result of various despeckling techniques with proposed technique for Synth.tif. Regarding the noise suppression performance, the proposed method shows a stable behavior with respect to the tuning parameter. It can also be seen that the window size 3*3 is optimal under the assumed speckle model. The enhanced Wavelet based method when compared to the Frost filter and Pizurica Method, outperforms these filters. The proposed method reduces the noise significantly by preserving the important details or features on several ultrasound images. The experimental results show that the proposed method yields significantly better visual quality and better values of SNR, EPI, MSE and COC [20] as compared to other techniques for speckle noise reduction. 6. EXPERIMENTAL RESULT 6.1 Image quality evaluation metrics For judging the performance of speckle suppression techniques various quality metrics are used:- Signal-to-Noise Ratio (SNR) Signal-to-Noise Ratio known as SNR value is defined as ration of desired signal to the background noise. It is calculated using the following expression. SNR= 10 log 10 (σ 2 g/σ 2 e) (8) where σ 2 g is variance of noise free reference image and σ 2 e is noise variance. SNR should be large for good quality image. Coefficient of Correlation (COC) Coefficient of Correlation (Narayanan and Wahidabanu, 2009) is measure of similarity between the original noise free reference image and denoised image. COC is calculated by: COC = Σ (I-I ) Σ (F-F ) (9) Σ (I-I ) 2 Σ(F-F ) 2 where I and I are the original and denoised image, F and F are mean of original and denoised image respectively. The value of COC should be near to unity for good quality image. Volume 1, Issue 2, July 2013 Page 33

6 Edge Preservation Index (EPI) Edge Preservation Index (EPI) (Narayanan and Wahidaban, 2009) is used to measure the filters edge preservation ability and is calculated as: EPI= Σ (ΔI-ΔI ) Σ (ΔF-ΔF ) (10) Σ (ΔI-ΔI ) 2 Σ (ΔF-ΔF ) 2 where, ΔI and ΔF are high-pass filtered versions of images I and F, obtained with a 3 3 pixel standard approximation of Laplacian operator. The larger value of EPI indicates more ability of filter to preserve edges. Mean Square Error (MSE): The MSE values are calculated using the following expression (Narayanan and Wahidaban,2009): MSE = 1 (11) M N 2 [s(i, j) s(i, j)] i 1 j 1 MXN where s(i,j) is original image and ŝ(i,j) is the denoised image. The lower the MSE value, the better image quality. 6.2 Experimental Results on image Ultrasound images are corrupted by speckle noise which affects all coherent imaging systems. Fig. 2 illustrates the examples of gradual speckle suppression using the proposed method. The results in this figure correspond to the window size 3*3 and different values of the tuning parameter. The results demonstrate that the increase of k leads to a stronger suppression of the background texture and to the enhancement of sharp intensity variations. To investigate the quantitative performance of the method, images with artificial speckle noise is used. A speckled image d= {d1..dn} is commonly modeled as [7] d k = f k v k, where f= {f1 fn} is a reference noise-free image and v = {v1..vn} is a unit mean random field. Two types of reference noise-free images are used: 1) realistic ultrasound images from Fig. 3, in which natural speckle noise was previously suppressed by the proposed method and 2) a simulated ultrasound image in Fig. 4, which consists of regions with uniform intensity, sharp edges, and strong scatterers. To see the qualitatively as well as quantitatively performance of the proposed algorithm, some experiments are conducted on several ultrasound images. The performance of the enhanced Wavelet based despeckling method for medical ultrasound images is compared with the results obtained from Frost filter, and Pizurica Method. For objective evaluation, the Signal-to-Noise Ratio (SNR), Edge Preservation Index (EPI), Coefficient of Correlation (COC) and Mean Square error (MSE) are used as given in Table 1. Table 1 IMAGE QUALITY EVALUATION METRICS FOR THE RESULTS Method Frost Filter Pizurica Method Proposed Method Metrics SNR EPI COC MSE CONCLUSION In this paper, a new, robust and efficient wavelet domain denoising technique is proposed. The enhanced Wavelet based method when compared to the Frost filter and Pizurica Method, outperforms these filters. The proposed method reduces the noise significantly by preserving the important details or features on several ultrasound images. The experimental results show that the proposed method yields significantly better visual quality and better values of Signal-to-Noise Ratio, Edge Preservation Index, Mean Square Error and Coefficient of Correlation as compared to other techniques for speckle noise reduction. Thus the proposed method reduces speckle noise and also preserves edges while despeckling in Volume 1, Issue 2, July 2013 Page 34

7 a better way than other techniques. The proposed method is of low-complexity, both in its implementation and execution time. It adapts itself to unknown noise distributions and to the local spatial image context. REFERENCES [1.] S. G. Chang, B. Yu, and M. Vetterli, Spatially adaptive wavelet thresholding with context modeling for image denoising, IEEE Trans. Image Processing, vol. 9, pp , Sept [2.] X. Li and M. Orchard, Spatially adaptive denoising under overcomplete expansion, presented at the IEEE Int. Conf. Image Processing, Vancouver, BC, Canada, Sept [3.] A. Pizurica, Image denoising using wavelets and spatial context modeling, Ph.D. dissertation, Ghent Univ., Ghent, Belgium, [4.] M. Jansen and A. Bultheel, Geometrical priors for noisefree wavelet coefficient configurations in image denoising, in Bayesian Inference inwavelet Based Models, P. Müller and B. Vidakovic, Eds. New York: Springer- Verlag, 1999, pp [5.] A. Pizurica, W. Philips, I. Lemahieu, and M. Acheroy, Despeckling SAR images using wavelets and a new class of adaptive shrinkage functions, in IEEE Int. Conf. Image Processing, Thessaloniki, Greece, Oct [6.] A. Pizurica, W. Philips, I. Lemahieu, and M. Acheroy, A joint interand intrascale statistical model for Bayesian wavelet based image denoising, IEEE Trans. Image Processing, vol. 11, pp , May [7.] A. Achim, A. Bezerianos, and P. Tsakalides, Novel Bayesian multiscale method for speckle removal in medical ultrasound images, IEEE Trans. Med. Imag., vol. 20, pp , Aug [8.] A. K. Jain, Fundamental of Digital Image Processing. Upper Saddle River, NJ: Prentice-Hall, [9.] M. K. Mihçak, I. Kozintsev, K. Ramchandran, and P. Moulin, Lowcomplexity image denoising based on statistical modeling of wavelet coefficients, IEEE Signal Processing Lett., vol. 6, pp , Dec [10.] Pizurica, A., Philips, W., Lemahieu, I., and Acheroy, M.(2003), A Versatile Wavelet Domain Noise Filtration Technique for Medical Imaging, IEEE Transactions on medical imaging, Vol. 22, no. 3 pp [11.] M. I. H. Bhuiyan, M.O. Ahmad and M.N.S. Swamy (2007), New Spatially Adaptive Wavelet-based Method for the Despeckling of Medical Ultrasound Images. IEEE Trans, pp [12.] Y. Chen and A. Raheja (2005), Wavelet Lifting for Speckle Noise Reduction in Ultrasound Images IEEE Engineering in Medicine and Biology 27th Annual Conference Shanghai, China,pp [13.] G.Y. Chen, T.D. Bui and Krzyzak,A.,(2005) Image denoising using neighbouring wavelet coefficients Integrated Computer-Aided Engineering 12 pp [14.] B. Deka and P.K. Bora (2009), A Versatile Statistical Model for Despeckling of Medical Ultrasound Images IEEE Trans on Image Processing,pp 1-4. [15.] B. Deka and P.K. Bora.(2010), Despeckling of Medical Ultrasound Images using Sparse Representation, IEEE Trans on Image Processing, pp 1-4. [16.] Michailovich,O.V. and Tannenbaum,A.(2006), Despeckling of Medical Ultrasound Images IEEE transactions on ultrasonics, ferroelectrics, and frequency control, vol. 53, no. 1, pp [17.] Mukkavilli,R. K., Sahambi,J. S. and Bora P.K.(2008), Modified homomorphic wavelet based despeckling of medical ultrasound images IEEE Trans,pp [18.] Mohideen,S.K., Perumal,S.A., Krishnan,N. and Selvakumar,R.K.(2010), A novel approach for image denoising using dynamic tracking with new threshold technique IEEE Trans, pp [19.] Narayanan,S.K. and Wahidabanu,R.S.D.(2009), A View on Despeckling in Ultrasound Imaging, International Journal of Signal Processing, Image Processing and Pattern Recognition Vol. 2, No.3,pp [20.] Narayanan,S.K. and WahidabanuR.S.D.(2010), Despeckling of medical diagonostic ultrasound images via laplacian based mixed pde IEEE Trans. in ICCCCT, pp [21.] Sudha, S., Suresh, G.R. and Sukanesh, R. (2009), Comparative Study on Speckle Noise Suppression Techniques for Ultrasound Images, International Journal of Engineering and Technology, Vol. 1, No. 1, pp [22.] Rabbani, H., Vafadust, M., Abolmaesumi, P. and Gazor, S.(2008), Speckle Noise Reduction Of Medical Ultrasound Images in Complex Wavelet Domain Using Mixture Priors, IEEE Transactions on biomedical engineering, Vol. 55, No. 9, pp Volume 1, Issue 2, July 2013 Page 35