survey of despeckling techniques for medical …...survey of despeckling techniques for medical...

Survey of Despeckling Techniques for Medical Ultrasound Images

Jappreet Kaur M.tech Computer Science,

Department Of CSE, Guru Nanak Dev Engineering College, Ludhiana (Punjab),

India. [email protected]

Jasdeep Kaur M.tech Computer Science,



Manpreet Kaur M.tech Computer Science,



Abstract Ultrasound imaging is the most commonly used imaging system in medical field. Main problem related to this imaging technique is introduction of speckle noise, thus making the image unclear. The success of ultrasonic examination depends on the image quality which is usually retarded due to speckle noise. There have been several techniques for effective suppression of speckle noise present in ultrasound images. This paper presents a review of some significant work carried out for despeckling of ultrasound images.

Keywords: Image denoising, ultrasound images, speckle noise, standard speckle filters, wavelet transform.

1. Introduction Ultrasound imaging being inexpensive, nonradioactive, real-time and non-invasive, is most widely used imaging system in medical field. To achieve the best possible diagnosis it is important that medical images be sharp, clear and free of noise and artifacts. However occurrence of speckle is a problem with ultrasound imaging. Speckle is the artifact caused by interference of energy from randomly distributed scattering [1]. Speckle noise tends to reduce image resolution and contrast and blur important details, thereby reducing diagnostic value of this imaging modality. Therefore speckle noise reduction is an important prerequisite whenever ultrasound imaging is used. Denoising of ultrasound images however still remains a challenge because noise removal causes blurring of the ultrasound

images. Sometimes physicians prefer to use original noisy images rather than filtered ones because of loss of important features while denoising. Thus appropriate method for speckle suppression is needed which enhances the signal to noise ratio while conserving the edges and lines in images. Speckle is generally considered to be multiplicative in nature. Within each resolution cell a number of elementary scatterers reflect the incident wave towards 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 modelled as ν1=ƒ1υ : where ƒ = { ƒ1, ƒ2, ƒ3,………ƒn } is a noise-free ideal image, ν = {ν1, ν2, ν3,….…νn } is speckle noise and υ = {υ1, υ2, υ3,……υ n } is a unit mean random field. [2] The paper is organised as follows: In section 2 various standard speckle filters are explained. Section 3 contains a description of wavelet based filtering techniques. Paper concludes with section 4 containing discussion of various despeckling techniques. 2. Standard Despeckling techniques There are many speckle reduction filters available, some give better visual interpretations while others have good noise reduction or smoothing capabilities. Some of the best known speckle reduction filters are

Jappreet kaur et al, Int. J. Comp. Tech. Appl., Vol 2 (4), 1003-1007

IJCTA | JULY-AUGUST 2011 Available [email protected]

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Median, Lee, Kuan, standard Frost, Enhanced Frost, Weiner, Gamma MAP and SRAD filters. Some of these filters have unique speckle reduction approach that performs spatial filtering in a square-moving window known as kernel. The filtering is based on the statistical relationship between the center pixel and its surrounding pixels. The typical size of filter window can range from 3-by-3 to 33-by-33, but the size of window must be odd. If the size of the filter window is too large, important details will be lost due to over smoothing. On the other hand, if the size of the window is too small, speckle reduction may not yield good results. Generally a 3-by-3 or 7-by-7 window is used giving good results [3]. 2.1 Median Filter

The Median Filter [4] computes the median of all the pixels within a local window and replaces the center pixel with this median value. Median filtering is a non-linear filtering technique. This method is effective in cases when the noise pattern consists of strong, spike like components and the characteristics to be preserved are edges. The main disadvantage of the median filter is the extra computation time needed to sort the intensity value of each set. 2.2 Wiener filter The Wiener Filter [5], also known as Least Mean Square filter, is given by the following expression: H(u, v) is the degradation function and H(u, v)* is its conjugate complex. G(u, v) is the degraded image. Functions Sf(u, v) and Sn(u, v) are power spectra of original image and the noise. Wiener Filter assumes noise and power spectra of object a priori.

𝑓𝑓(𝑢𝑢,𝑣𝑣 ) = � 𝐻𝐻(𝑢𝑢 ,𝑣𝑣)∗

𝐻𝐻(𝑢𝑢 ,𝑣𝑣)2 + �Sn(u,v)Sf(u,v)� �

� G(u, v) (1)

2.3 Lee Filter Lee Filter[6] is based on multiplicative speckle model and it can use local statistics to effectively preserve edges. This filter is based on the approach that if the variance over an area is low or constant, then smoothing will not be performed, otherwise smoothing will be performed if variance is high(near edges). Img(i, j) = Im + W ∗ (Cp − Im) (2)

Where Img is the pixel Value at indices i, j after filtering, Im is mean intensity of the filter window, Cp is the center pixel and W is a filter window given by:

W = σ2 (σ2 + ρ2 )⁄ (3) where σ2 is the variance of the pixel values wihin the filter window and is calculated as:

σ2 = �1 N∑ �Xj�2N−1

j=0⁄ � (4) Here, N is the size of the filter window and Xj is the pixel value within the filter window at indices j. The parameter ρ is the additive noise variance of the image given in following equation, where M is the size of the image and Yj is the value of each pixel in the image.

ρ2 = �1 M∑ (Yi)2M−1i=0⁄ � (5)

If there is no smoothening, the filter will output only the mean intensity value(Im) of the filter window. Otherwise, the difference between Cp and Im is calculated and multiplied with W and then summed with Im. The main drawback of Lee filter is that it tends to ignore speckle noise near edges. 2.4 Kuan Filter

Kuan filter[7] is a local linear minimum square error filter based on multiplicative order it does not make approximation on the noise variance within the filter window like lee filter it models the multiplicative model of speckle noise into an additive linear form. The weighting function W is computed as follows: 𝑊𝑊 = (1− 𝐶𝐶𝑢𝑢/𝐶𝐶𝑖𝑖)/(1 + 𝐶𝐶𝑢𝑢) (6) The weighting function is computed from the estimated noise variation coefficient of the image, Cu computed as follows: 𝐶𝐶𝑢𝑢 = �1/𝐸𝐸𝐸𝐸𝐸𝐸 (7) And Ci is the variation coefficient of the image computed as follows: 𝐶𝐶𝑖𝑖 = 𝑆𝑆/𝐼𝐼𝐼𝐼 (8) Where S is the standard deviation in filter window and Im is mean intensity value within the window. The only limitation with Kuan filter is that the ENL parameter is needed for computation. 2.5 Frost Filter

Frost filter[8] is a spatial domain adaptive filter that is based on multiplicative noise order it adapts to noise variance within the filter window by applying exponentially weighting factors M as:



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𝑀𝑀𝑛𝑛 = exp(−(𝐷𝐷𝐷𝐷𝑀𝑀𝐷𝐷 ∗ (𝑆𝑆/𝐼𝐼𝐼𝐼)2) ∗ 𝑇𝑇) (9) The weighting factor decrease as the variance within the filter windows reduces. DAMP is a factor that determines the extent of the exponential damping for the image. The larger the damping value, the heavier is the damping effect. Typically the value is set to 1. S is the standard deviation of the filter window, Im is the mean value within the window and T is the absolute value of the pixel distance between the center pixel to its surrounding pixels in the filter window. The value of the filtered pixel is replaced with a value calculated from weighted sum of each pixel value Pn and the weights of each pixel Mn in the filter window over the total weighted value of the image as: 𝐼𝐼𝐼𝐼𝐼𝐼(𝑖𝑖, 𝑗𝑗) = ∑𝐷𝐷𝑛𝑛 ∗ 𝑀𝑀𝑛𝑛 /∑𝑀𝑀𝑛𝑛 (10) The parameters in the Frost filter are adjusted according to the local variance in each area. If the variance is low, then the filtering will cause extensive smoothing. Whilst in high variance areas, little smoothing occurs and edges are retained. 2.6 Enhanced Frost Filter

The Enhanced Frost filter[9] is an extension of the Frost filter that further divides the radar image into homogenous, heterogeneous and isolated point target areas. It applies a different exponentially weighting factor M in equation to optimally filter each region. 𝑀𝑀𝑛𝑛 = exp(−𝐷𝐷𝐷𝐷𝑀𝑀𝐷𝐷 ∗ (𝐶𝐶𝑖𝑖 − 𝐶𝐶𝑢𝑢\𝐶𝐶𝐼𝐼𝑚𝑚𝑚𝑚 − 𝐶𝐶𝑖𝑖) ∗ 𝑇𝑇 (11) Ci is the local coefficient of variation of the filter window Ci=S/Im (12) Cu is the speckle coefficient of variation of the image using equivalent number of looks. Cu = 1/√ENL (13) Cmax is the upper speckle coefficient of variation of the image. C𝐼𝐼𝑚𝑚𝑚𝑚 = �(1 + 2 𝐸𝐸𝐸𝐸𝐸𝐸)⁄ (14) The output of the filter divides the image into three classes depending on the comparison between the local coefficient of variation Ci in a defined window size and the speckle coefficient of variation Cu. If Ci is less than Cu, the speckle is removed by replacing the value of the filtered pixel with the intensity mean Im of the filter window. This represents the homogeneous or uniform class. In the second class, if Ci falls between the lower and upper speckle coefficient of variation, the value of filtered pixel is replaced by the total weighted value in equation.

Img(i, j) = ∑ Pn ∗ Mn/∑Mn (15) This represents the heterogeneous class where the speckle is reduced but not removed so as to preserve the quality of the image. In the last class,Ci is larger than the upper threshold Cmax. In this case, the value for the filtered pixel is replaced by the centre pixel within the filter window. This is due to the consideration that isolated points with high reflectivity should be kept for analysis. The Enhanced Frost filter in the comparison to the Frost filtering better preserves the edges and texture of an image. 2.7 Gamma/MAP Filter The focus of the Gamma or Maximum A Posteriori (MAP)[10] filter is to minimize the loss of texture information by assuming that the image of forested areas, agricultural lands, and oceans are gamma distributed scenes. This approach is better than the Frost and Lee filter and it uses the coefficient of variation and contrast ratio whose theoretical probability density function will determine the smoothing process. The algorithm is similar to Enhanced Frost filter except that if the local coefficient of variation Ci falls between the two thresholds Cu and Cmax, the filtered pixel value is based on the Gamma estimation of the contrast ratios within the appropriate filter window given in equation. Img(i, j) = ((W − ENL − 1) ∗ Im + √D)/(2 ∗ W) (16) Where W is the weighting function. W = (1 + Cu

2)/(Ci2 − Cu

2) (17) And D is give as

D=Im*Im*(W-ENL-1)*(W-ENL-1)+4*W*ENL*Im*Cp (18)

Ci is the speckle coefficient of variation of the filter window.

Ci=S/Im (19) Cu is the speckle coefficient of variation of using equivalent number of looks Cu = 1/√ENL (20) Cmax is the upper speckle coefficient of variation of image. C𝐼𝐼𝑚𝑚𝑚𝑚 = √2 ∗ 𝐶𝐶𝑢𝑢 (21) If Ci is smaller than Cu the value of the filtered pixel within the filter window will be replaced by mean of filter window. If Ci is greater than Cmax then the value of filtered pixel will be replaced by center pixel in the filtered window.



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2.8 SRAD Filter

SRAD[11] is a Partial Differential Equation (PDE) approach to spackle removal in images. The PDE-based speckle removal approach allows the generation of an image scale space (a set of filtered images that vary from fine to coarse) without bias due to filter window size and shape. Basic theory: SRAD is an anisotropic diffusion method for smoothing speckled imagery. Given an intensity image 𝐼𝐼0(𝑚𝑚,𝑦𝑦) having finite power and no zero values over the image support Ω, the output image I(x, y; t) is evolved according to the following PDE:

�𝜕𝜕𝐼𝐼(𝑚𝑚, 𝑦𝑦; 𝑡𝑡)/𝜕𝜕𝑡𝑡 = 𝑑𝑑𝑖𝑖𝑣𝑣[𝑐𝑐(𝑞𝑞)∆𝐼𝐼(𝑚𝑚,𝑦𝑦; 𝑡𝑡)]

𝐼𝐼(𝑚𝑚, 𝑦𝑦; 0) = 𝐼𝐼0(𝑚𝑚, 𝑦𝑦), (𝜕𝜕𝐼𝐼(𝑚𝑚,𝑦𝑦; 𝑡𝑡)/𝜕𝜕𝑛𝑛�⃗ )|𝜕𝜕Ω = 0

� (22)

Where 𝜕𝜕Ω denotes the border of , 𝑛𝑛�⃗ is the outer normal to the 𝜕𝜕Ω, and 𝑐𝑐(𝑞𝑞) = 1

1+�𝑞𝑞2(𝑚𝑚 ,𝑦𝑦 ;𝑡𝑡)−𝑞𝑞0 2 (𝑡𝑡)�/[𝑞𝑞0

2(𝑡𝑡)(1+𝑞𝑞02(𝑡𝑡))]

(23)

Or 𝑐𝑐(𝑞𝑞) = exp{−[𝑞𝑞2(𝑚𝑚, 𝑦𝑦; 𝑡𝑡) − 𝑞𝑞0

2(𝑡𝑡)]/[𝑞𝑞02(𝑡𝑡)(1 + 𝑞𝑞0

2(𝑡𝑡))]} (24)

In (23) and (24), q(x, y; t) is the instantaneous coefficient of variation determined by

𝑞𝑞(𝑚𝑚, 𝑦𝑦; 𝑡𝑡) = ��1

2��|Δ𝐼𝐼|𝐼𝐼 �

2−� 1

42��Δ2𝐼𝐼𝐼𝐼 �

2

�1+�14��

Δ2𝐼𝐼𝐼𝐼 ��

2 (25)

and 𝑞𝑞0(𝑡𝑡) is the speckle scale function. In the SRAD, the instantaneous coefficient of variation q(x, y; t) serves as the edge detector in spackled imagery. The function exhibits high values at edge or on high-contrast features and produces low values in homogenous regions. The modification reflects encouraging isotropic diffusion in homogenous regions of the image where q(x, y; t) fluctuates around 𝑞𝑞0(𝑡𝑡). The speckle scale function 𝑞𝑞0(𝑡𝑡) effectively controls the amount of smoothing applied to the image by SRAD. It is estimated using

𝑞𝑞0(𝑡𝑡) = �𝑣𝑣𝑚𝑚𝑣𝑣 [𝑧𝑧(𝑡𝑡)]𝑧𝑧(𝑡𝑡)�� (26)

Where var[z(t)] and 𝑧𝑧(𝑡𝑡)�� are the intensity variance and mean over a homogenous area at t, respectively.

3. Wavelet Filters 3.1 Wavelet Thresholding Speckle noise is a high-frequency component of the image and appears in wavelet coefficients. One widespread method exploited for speckle reduction is wavelet thresholding procedure. Basic procedure for all thresholding method is

1. Calculate DWT if the Image. 2. Threshold the wavelet components. 3. Compute IDWT to obtain denoised estimate.

There are two thresholding functions frequently used i.e. Hard Threshold, Pan et al. [12], Soft threshold. Hard-Thresholding function keeps the input if it is larger than the threshol ; otherwise, it is set to zero. Soft-thresholding function takes the argument and shrinks it toward zero by the threshold. Soft-thresholding rule is chosen over hard-thresholding, for the soft-thresholding method yields more visually pleasant images over hard thresholding. A result may still be noisy. Large threshold alternatively, produces signal with large number of zero coefficients. This leads to a smooth signal. So much attention must be paid to select optimal threshold. Achim et.al [13], Thitimajshima.P et.al [14] suggested speckle reduction through wavelet transform based on Bayesian approach by means of the statistical models of both noise and signal. Wavelet-based denoising using Hidden Markov Trees, initially proposed by Crouse, et. al. [15], Romberg, et. al. [16] has been quite successful, and gave rise to a number of other HMT and used the minimum mean-squared error (MMSE) - like estimators for suppressing the noise. Some of the wavelet shrinkages are as follows. 3.2 Universal Threshold

Donoho in his work[17],[18] proposed Universal threshold (Visu Shrink) that over-smooth images. Universal threshold 𝑇𝑇 = 𝜎𝜎�2 log n, with n equal to size of the image, σ is noise variance. This was determined in an optimal context for soft thresholding with random Gaussian noise. This is easy to implement but provides a threshold level larger than with other decision criteria, resulting in smoother reconstructed data. This estimation does not allow for the content of the data, but only depends on the data size n. Also threshold tends to be high for large values of M, killing many signal coefficients along with the noise. Thus, the threshold does not adapt well to discontinuities in the signal.



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3.3 Stein Unbiased Estimated of Risk (SURE) The Universal threshold was later improved by Donoho[18] using the SURE threshold. It is sub band adaptive and is derived by minimizing Stein’s unbiased risk estimator. Stein’s result to get an unbiased estimate of the risk 𝐸𝐸��̂�𝜇(𝑡𝑡)(𝑚𝑚)− 𝜇𝜇2� : SURE(𝑡𝑡;𝑚𝑚) = 𝑑𝑑𝑑𝑑 − 2#{𝑖𝑖 = |𝑚𝑚𝑖𝑖 | < 𝑇𝑇} +∑ min(|𝑚𝑚𝑖𝑖,𝑡𝑡 |)𝑑𝑑

𝑖𝑖=12

(27) For an observed vector x the threshold ts is found that minimizes SURE (t;x), i.e.

ts=Arg mint SURE(t;x) The above optimization is computationally straightforward. 4. Discussion The comparative study of various speckle reducing filters for ultrasound images shows that wavelet filters outperforms the other standard speckle filters. Although all standard speckle filters perform well on ultrasound images but they have some constraints regarding resolution degradation. These filters operate by smoothing over a fixed window and it produces artifacts around the object and sometimes causes over smoothing. Wavelet transform is best suited for performance because of its properties like sparsity, multiresolution and multiscale nature. Thresholding techniques used with discrete wavelet are simplest to implement. References: [1]Example of “Speckle Reduction In Ultrasound Imaging”, [Online] Available: http://www.ljbdev.com/speckle.html. [2] S.Sudha, G.R.Suresh, R.Sukanesh , “Speckle Noise Reduction in Ultrasound Images by Wavelet Thresholding based on Weighted Variance”, International Journal of Engineering and Technology Vol. 1, No. 1, April, 2009, 1793-8201. [3] Hong Sern Tan, “ Denoising of Noise Speckle in Radar Image”, Oct. 2001. [4] R.Fisher; Median Filter”, [Online] http://www.dai.edu.ac.uk/HIPR2/median.htm, September, 2001. [5] T. Kailath, “Equations of Wiener-Hopf type in filtering theory and related applications,” in Norbert Wiener: Collected Works vol. III, P.Masani, Ed. Cambridge, MA: MIT Press, 1976, pp. 63–94. [6] J. S. Lee, “Digital image enhancement and noise filtering by use of local statistics,” IEEE Trans.

[7] D. T. Kuan, A. A. Sawchuk, T. C. Strand, and P. Chavel, “Adaptive noise smoothing filter for images with signal-dependent noise,” ,IEEE Trans. [8] V.S.Frost, J.A.Stiles, K.S.Shanmugam, J.C.Holtzman, ”A model for radar image & its application to Adaptive digital filtering for multiplicative noise”, IEEE Transaction on pattern analysis and machine intelligence, Vol.PMAI 4, pp.175-166, 1982. [9] A. Lopes et. al., “Adaptive speckle filters and Scene heterogeneity”, IEEE Transaction on Geoscience and Remote Sensing, Vol. 28, No. 6, pp. 992-1000, Nov. 1990. [10] Lopes.A, Nesry.E, Touzi.R, Laur.H., “Maximum A Posteriori speckle filtering and first order texture models in SAR images”. Proceedings of IGARSS’ 90, May 1990, vol. 3 (Maryland: IGARSS), pp. 2409–2412, 1990. [11] S. T. Acton, "Deconvolutional Speckle Reducing Anisotropic Diffusion," presented at Image Processing, 2005. ICIP 2005. IEEE International Conference on, 2005. [12] Q. Pan “Two denoising methods by wavelet transform,“ IEEE Trans Signal Processing, vol. 47, pp. 3401-3406, Dec. 1999. [13] J.S. Lee, ‘Refined filtering of image noise using local statistics‘, Computer Vision, Graphics and Image Processing. [14] Thitimajshima. P, Rangsanseri. Y, and Rakprathanporn. P, “A Simple SAR Speckle Reduction by Wavelet Thresholding ”, Proceedings of the 19th Asian Conference on Remote Sensing ACR98, pp. P-14-1 – P-14-5, 1998. [15] Crouse, M.S., R.D. Nowak, R.G. Baraniuk, “Wavelet based statistical signal Processing using Markov models”, IEEE Trans. Signal Processing, Vol.46, no. 4, pp. 886-902, 1998. [16] J.Romberg, H.Choi and R.G. Baraniuk (1999),”Bayesian tree-structured image modelling using wavelet – based hidden Markov models”, in SPIE Technical Conference On Inverse Mathematical Problem modelling, Bayesian, and, Denver, Colorado. [17] D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation via wavelet shrinkage,” Biometrika, vol. 81, pp. 425-455, 1994. [18] D. L. Donoho and I. M. Johnstone , ”Adapting to unknown smoothness via wavelet shrinkage” J. Amer. Statist. Assoc. , vol. 90, pp. 1200-1224, December 1995.



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survey of despeckling techniques for medical …...survey of despeckling techniques for medical...

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