Denoising using Curvelet Transform with Improved Thresholds for Application on Ultrasound Images

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1 7 Denoising using Curvelet Transorm with Improved Thresholds or Application on Ultrasound Images Er. Tainder Kaur, Assistant Proessor, SBBSIET Padhiana, alandhar Er. Harpreet Kaur, Assistant Proessor, SBBSIET Padhiana, alandhar ABSTRACT In the medical literature, speckle has been treated as a distracting artiact as it tends to degrade the resolution and the obect detect ability. In medical image processing, image denoising has become a very essential exercise all through the diagnose. Negotiation between the preservation o useul diagnostic inormation and noise suppression must be treasured in medical images. In case o ultrasonic images a special type o acoustic noise, technically known as speckle noise, is the maor actor o image quality degradation. Many denoising techniques have been proposed or eective suppression o speckle noise. Removing noise rom the original image or signal is still a challenging problem or researchers. In this paper, a Curvelet transorm based denoising with improved thresholds is proposed or ultrasound images. Keywords Image Denoising; Curvelet Transorm; Ultrasound Images: Speckle noise. I. INTRODUCTION A. Motivation Noise elimination is a main concern in computer vision and image processing. For example, in many applications where operators based on computing image derivatives are applied, any noise in the image can result in serious errors. Noise presence is maniested by undesirable inormation, not related to the scene under study, which perturbs the inormation relative to the orm observable in the image. It is translated into more or less severe values, which are added or subtracted to the true gray level values on a number o pixels. Noise can appear in images rom a variety o sources: during the acquisition process, due to cameras quality, and resolution, but also due to the acquisition conditions, such as the illumination level, calibration and positioning. Moreover, it can be a unction o the scene environment: background, shape composition, material nature, etc. Noise distribution in the image varies considerably interand in images. Noise can be inserted into the image signal in dierent ways. It can be random and coherent with this signal. In this case, it is included inside the spatial requency domain o the image and cannot be suppressed other than by using a priori knowledge about the image. This oten produces a loss in spatial resolution. I the noise is periodic, it is out o the useul inormation, and its suppression is oten easy without inormation lost. Finally, when the captor provides a repetitive and redundant signal, which is normally the case or moving scenes, the noise present is said to be incoherent with the inormation being sought and can be easily eliminated. ong-sen Lee [] has proposed the computational techniques involving contrast enhancement and noise iltering on two-dimensional image arrays are developed based on their local mean and variance. These algorithms are no recursive and do not require the use o any kind o transorm. V. V. Frost et al. have proposed the standard image processing techniques which are used to enhance no coherent optically produced images are not applicable to radar images due to the coherent nature o the radar imaging process []. Piotr S. Windyga has proposed a generic -dimensional ilter with the primary purpose o eliminating impulsive-like noise is presented. This recursive nonlinear ilter is composed o two conditional rules, which are applied independently, in any order, one ater the other [3]. Yongian Yu and Scott T. Acton have proposed speckle reducing anisotropic diusion (SRAD), a diusion method tailored to ultrasonic and radar imaging applications. SRAD is the edge-sensitive diusion or speckled images, in the same way that conventional anisotropic diusion is the edge-sensitive diusion or images corrupted with additive noise [4]. ean-luc Starck et al. have proposed the radon, ridgelet and curvelet transorms or image denoising. They apply these digital transorms to the denoising o some standard images embedded in white noise [5]. S.Sudha. et al. have proposed the wavelet based image denoising using adaptive thresholding which describes a new method or suppression o noise in image by using the wavelet Denoising technique with optimized thresholding unction, improving the denoised results signiicantly [6]. M.Singh et al. described a comparative study o various spatial domain ilters or speckle suppression in Ultrasound images [7]. K.R.oshi et al proposed the quality metrics or speckle in coherent imaging and their limitations. It also describes a new metric-sdi, its uniqueness in quantiying the speckle and comparison o perormance with existing metrics [8]. Li Hongqiao and W.Shengqian have proposed a new method o wavelet based image denoising with sotthresholds [9]. M.N. Nobi et al. proposed an eicient and simple method or noise reduction rom medical images.

2 8 They modiied median ilter by adding more eatures [0]. Rayudu et al. have proposed the curve let transorm or ultrasound image denoising. Speckle reduction/iltering i.e. visual enhancement techniques are used or enhancing the visual quality o the images []. B. Main Contribution To overcome the limitations o SRAD Filter and wavelet transorm, the curvelet transorm is proposed or denoising o ultrasound images with improved thresholds or preserving and enhance the edges. The perormance o each ilter will be compared using parameter PSNR (Peak Signal to Noise Ratio). The organization o the paper as ollows: In section I, a brie review o image denoising and related work is given. Section II, presents a concise review o curvelet transorm. Section III, presents the thresholding methods or image denoising and proposed system ramework. Experimental results and discussions are given in section IV. Based on above work conclusions are derived in section V. II. CURVELET TRANSFORM (CT) Curvelet Transorm Techniques: Curvelet Transorm is a new multi-scale representation most suitable or obects with curves. Developed by Candès and Donoho (999).A discontinuity point aects all the Fourier coeicients in the domain. Hence the FT doesn t handle point s discontinuities well. Using wavelets, it aects only a limited number o coeicients. Hence the WT handles point discontinuities well. A discontinuity across a simple curve aects all the wavelets coeicients on the curve. Hence the WT doesn t handle curves discontinuities well. Curvelets are designed to handle curves using only a small number o coeicients. Hence the CvT handles curve discontinuities well. The Curvelet Transorm includes our stages: Sub-band decomposition Smooth partitioning Renormalization Ridgelet analysis C. Radon Transorm The Radon transorm o an obect is the collection o line integrals indexed by (, t) [0, ) Rgiven by R (, t) ( x, x ) ( x cos x sin t) dx dx () where δ is the Dirac distribution. The ridgelet coeicients CRT ( a, b, ) o an obect are given by analysis o the Radon transorm via / CRT ( a, b, ) R (, t) a (( t b) / a) dt () Basic algorithm or discrete radon transorm is as ollows. Compute the two-dimensional Fast Fourier Transorm (FFT) o unction.. Using an interpolation scheme, substitute the sampled values o the Fourier transorm obtained on the square lattice with sampled values o ˆ on a polar lattice: that is, on a lattice where the points all on lines through the origin. Compute the one-dimensional Inverse Fast Fourier Transorm (IFFT) on each line; i.e., or each value o the angular parameter. D. Discrete Ridgelet Transorm (DRT) A continuous ridgelet transorm is calculated by applying D wavelet transorm to the slices o radon transorm R (,.). In radon transorm a amous proection-slice theorem is used ˆ( cos, sin ) (, ) i x R t e dt (3) This theorem says that the Radon transorm can be obtained by applying the one-dimensional inverse Fourier transorm to the two-dimensional Fourier transorm o unction restricted to radial lines through the origin. The relation among the Fourier, radon and ridgetet domain is depicted in Fig.. To complete the ridgelet transorm, apply a onedimensional wavelet transorm along the radial variable in Radon space. The sum up o above procedure is shown in Fig. in the orm o low chart. The DRT o an image o size n n is an image o size n n, introducing a redundancy actor equal to 4 [5]. Fig. : Relations between transorms Fig. : Flowchart o Discrete ridgelet transorms

3 9 E. Curvelet Transorm The idea o Curvelet (Starck et al, [5]) is to represent a curve as a superposition o unctions o various lengths and widths obeying the scaling law width length. this can be done by irst decomposing the image into subbands, i.e., separating the obect into a series o disoint scales. Each scale is then analysed by means o a local ridgelet transorm. Recently, Starck et al. [5] showed that `a trous subband iltering algorithm [] is especially well-adapted to the needs o the digital Curvelet transorm. The algorithm decomposes an n by n image I as a superposition o the orm I( x, y) c ( x, y) ( x, y) (4) Where represents the details o I at scale. Thus, the algorithm outputs + sub band arrays o size n n. [The indexing is such that, here, = corresponds to the inest scale (high requencies).] Curvelet Transorm Algorithm Starck et al. [5] presented a sketch o the discrete Curvelet transorm algorithm:. apply the `a trous algorithm with scales [];. set B Bmin ; 3. or =,..., do i) partition the subband with a block size B and apply the digital ridgelet transorm to each block; ii) i modulo = then B B ; iii) else B B ; Note that the coarse description o the image c is not processed. Fig. 3 gives an overview o the organization o the algorithm. Extensive literature o Curvelet Transorm theory can be ound in the reerence [5]. III. IMAGE DENOISING F. Denoising by Hard Thresholding Suppose that one is given noisy data o the orm: I ( x, y) I( x, y) Z( x, y) (5) Where Z(x,y) is unit-variance and zero-mean Gaussian noise. Denoising a way to recover I(x,y) rom the noisy image I ( x, y ) as proper as possible. Rayudu et al. [] have proposed the hard thresholds or Ultrasound image denoising as shown below: Let y λ be the noisy Curvelet Coeicients (y = C*I). They used the ollowing hard-thresholding rule or estimating the unknown Curvelet coeicients: yˆ y ; i y k (6) yˆ 0; else In their experiments, they have chosen a scale dependent value or k; k = 4 or the irst scale ( = ) while k = 3 or the others ( > ). Algorithm:. Apply Curvelet transorm to the noisy image and get the scaling coeicients and Curvelet coeicients.. Chose the threshold by Eq. (6) and apply thresholding to the Curvelet coeicients (leave the scaling coeicients alone). 3. Reconstruct the scaling coeicients and the Curvelet coeicients threshold and get the denoised image. Fig. 3 Curvelet transorm low graph G. Proposed Thresholding algorithm The hard thresholding is ineective in many examples. Though the NeighCoe [3] scheme which considers neighboring Curvelet coeicients to be proposed in this work. In this scheme, the size o neighbor varies with the dependence o the coeicients. N, k, k n; 0 nn S C N N (7) Here is the level in curvelet decomposition and (N+) is the size o neighbor. N 0 can be selected according to the size o image and the support o the Curvelet coeicents: C C 0 i S, k, k k, S k, else where is given by logn and α is a parameter that adusts the threshold. (8)

4 0 Fig. 4: (irst column) sample images, (second column) noisy images, (third column) denoising results o SRAD technique, (ourth column) denoising results o wavelet transorm technique, (ith column) and denoising results o curvelet transorm with hard thresholding (sixth column) denoising results o the proposed method. H. Proposed Denoising Algorithm Algorithm:. Apply Curvelet transorm to the noisy image and get the scaling coeicients and Curvelet coeicients.. Chose the threshold by Eq. (8) and apply thresholding to the Curvelet coeicients (leave the scaling coeicients alone). 3. Reconstruct the scaling coeicients and the Curvelet coeicients threshold and get the denoised image. IV. EXPERIMENTAL RESULTS AND DISCUSSIONS Removal o noises rom the images is a critical issue in the ield o digital image processing. The phrase Peak Signal to Noise Ratio (PSNR), oten abbreviated PSNR, is an engineering term or the ratio between the maximum possible power o a signal and the power o corrupted noise that aects the idelity o its representation. As many signals have wide dynamic. The MSE and PSNR are deined as:

5 55 PSNR 0log0 MSE MSE I i k i mn (8) m n (, ) (, ) (9) i0 0 Fig. 4 shows the denoising results o dierent methods on ive sample images. In Fig. 4, the irst column presents the ive sample ultrasound images; second column shows the sample images with Gaussian noise o zero mean and 0.0 variance; third, ourth ith, and sixth columns denote the denoising results o the SRAD, wavelet, Curvelet with hard thresholding and proposed method respectively. From Fig. 4, it is clear that the proposed method outperorming the SRAD, wavelet and Curvelet transorm with hard thresholding based denoising techniques. TABLE I DENOISING RESULTS OF VARIOUS METHODS IN TERMS OF PSNR UNDER GAUSSIAN NOISE OF ZERO MEAN AND 0.0 VARIANCE. Image No. SRAD Wavelets Curvelet with Hard Thresholding Proposed Method TABLE II DENOISING RESULTS OF VARIOUS METHODS IN TERMS OF PSNR UNDER GAUSSIAN NOISE OF ZERO MEAN AND 0.0 VARIANCE. Image No. SRAD Wavelets Curvelet with Hard Thresholding Proposed Method Table I & II show the results o dierent methods on ive sample images. From Table I & II, it is clear that the proposed method outperorming the SRAD and wavelet based denoising techniques. V. CONCLUSIONS A new thresholding algorithm is proposed in this paper or curvelet based image denoising on ultrasound images. The perormance o the proposed thresholding algorithm is compared with the SRAD, wavelet transorm and Curvelet transorm with hard thresolding. The results ater investigation show that the proposed method is outperorming the other existing methods in terms PSNR. REFERENCES []. S. Lee, Digital image enhancement and noise iltering by using local statistics, IEEE Trans. Pattern Anal. Machine Intell., vol. PAM-,980. [] V. S. Frost,. A. Stiles, K. S. Shanmugan, and. C. Holtzman, A model or radar images and its application to adaptive digital iltering o multiplicative noise, IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-4, pp , 98. [3] Piotr S. Windyga, Fast Impulsive Noise Removal, IEEE transactions on image processing, vol. 0, no.,pp [4] Yongian Yu and Scott T.Action, Speckle reducing anisotropic diusin, IEEE Trans.Image Processing, vol.,no., pp.60-70,00. [5] ean-luc starck, Emmanual.Candes, and David L.Donoho, The Curvelet transorm or image Denoising IEEE Trans.Image processing,vol.,no.6,pp ,00. [6] S.Sudha, G.R.Suresh and R.Sukanesh, wavelet based image denoising using Adaptive thresholding the International Conerence on Computational Intelligence and Multimedia Applications IEEE (007). [7] M. Singh, Dr.S.Singh, Dr. S.Kansal, Comparative Analysis o spatial ilters or speckle reduction in ultrasound images, World Congress on Computer Science and Inormation Engineering IEEE(008). [8] K.R.oshi, R.S.Kamathe, SDI: New metric or quantiication o speckle noise in ultrasound imaging IEEE (Nov 008). [9] [0] Li. Hongqiao, Wang Shengqian, A New Image Denoising Method Using Wavelet Transorm, International Forum on Inormation Technology and Applications IEEE(009). [0] M. N. Nobi and M. A. Yousu, A New Method to Remove noise in Magnetic Resonance and Ultrasound Images, ournal O Scientiic Research (00). [] D. K. V. Rayudu, Subrahmanyam Murala, and Vinod kumar, Denoising o Ultrasound Images using Curvelet Transorm, The nd International Conerence on Computer and Automation Engineering (ICCAE 00), Singapore, vol. 3, pp , 00. [] Yong-bing Xu, Chang-Sheng Xie, and Cheng-Yong Zheng, An Application o the á Trous Algorithm in Detecting Inrared Targets, IEEE con. on Wavelet Analysis and Pattern Recognition, Beiing, China, - 4: Nov. 007, pp [3] X. Wang, Y. Zi, and Z. He, Multiwavelet denoising with improved neighboring coeicients or applications on rolling bearing ault diagnosis,,. Mechanical Systems and Signal Processing vol. 5, pp , 0.