A Novel Image Denoising Algorithm for Suppressing Mixture of Speckle and Impulse Noise in Spatial Domain

Akshat Jain, Vikrant Bhateja Deptt. of Electronics & Communication Engg.

SRMCEM Lucknow (U.P.), India

jainakshatjain@yahoo.com, bhateja.vikrant@gmail.com

Abstract—This paper proposes a novel image denoising algorithm in spatial domain for filtering mixture of speckle and impulse noise using combination of local statistics and non-linear Robust Estimator. Proper choice of despeckling filter is an important requirement for contrast enhancement. On the other hand suppression of impulse noise aids the enhancement and preservation of edges. The proposed algorithm improves the local statistics approach for despeckling followed by application of Robust Estimator for efficient filtering of high density impulse noise. Peak Signal to Noise Ratio (PSNR) and Coefficient of Correlation (COC) are used as quality metrics for evaluating the performance of the proposed algorithm. Simulation results portray significant improvement in the restored image obtained after suppression of the noise mixture (speckle + impulse) along with preservation of local features in comparison to other algorithms. Keywords- COC; impulse noise; local statistics; robust estimator; speckle;

I. INTRODUCTION Data obtained by image sensors is generally

contaminated by noise because of localized hardware failures. Noise can be introduced in an image due to faulty acquisition process, interfering natural phenomenon, transmission errors and compression, which severely degrades the image quality, causes distortion and loss of information [1]-[2]. Noise, if remains unprocessed, makes the process of contrast enhancement, edge detection and segmentation less efficient and complicated. Noise suppression algorithms at times, may lack sensitivity, where the removal of noise is achieved at the cost of over smoothening, losing finer details and edge sharpness, thereby introducing artifacts [3]-[4]. The present work is based on developing filters which could jointly suppress both speckle and impulse noises. This type of mixed noise can contaminate an image when an already noisy image is transmitted over a channel. Speckle is a type of locally correlated multiplicative noise having a granular pattern [5]-[6]. This noise is common in coherent imaging systems like synthetic aperture radar imagery, laser, and ultrasound based imaging [7]. Impulse noise appears as a sprinkle of bright and dark spots and can take either the minimum or the maximum value in the dynamic range. This noise can lead to poor visualization [8]-[9] and may be caused by a variety of

factors such as: transmission channel error, edge sharpening procedures, sensor faults, engine sparks, atmospheric electrical disturbances, etc. [2], [10]. Images restored using linear filters, do not remove impulse noise effectively and also contain blurred edges. Non-linear filters like, standard median filter, remove this noise efficiently along with the preservation of edges but at the cost of some desirable details [3]. Median filters also modify the pixels not contaminated by noise which leads to the loss of finer image details causing edge jitter and streaking [11]. Some of the variations of the standard median filter are described in [12]-[15]. These filters identify the possible noisy pixels and replace them by the median value or its variants. They lack satisfactory reproduction of finer details and edges especially when the noise levels are high. Madhu et al. proposed a decision based algorithm [16] which used a 3x3 window for filtering, with a lower processing time. However, noise is not completely removed by this algorithm [16] at high density and there also occurs a heavy blurring. Jayaraj et al. presented a robust estimation technique [17] which efficiently removed the noise at low densities but reconstructed a poor quality image at higher densities using a maximum window size of 7x7. The method introduced blurring because of the usage of a large sized window. Speckle noise was initially removed by averaging of uncorrelated images of the same tissue recorded under different spatial positions [18]-[20]. These methods are effective for speckle reduction but they require multiple images of the same object which increases the cost [21]. Speckle noise reduction algorithms which use local statistics are given in [19], [21]-[25]. Images degraded by speckle noise when restored by median and weiner filter contain traces of noise along with blurred edges [26]. Christos P. Loizou et al. [27] compared the various existing despeckling filters and used both objective and subjective methods to validate the results. V. Ponomaryov et al. proposed an algorithm based on order statistics [28]. The processing time for this algorithm is low but the simulations were performed using a mixture of very low density impulse and speckle noises. Solbo et al. proposed a modified homomorphic filter [29], for removal speckle, although the visual quality of the denoised image was extremely poor. Rerona et al. proposed a non linear despeckling technique based on anisotropic diffusion [30], which required a lot of iterations as compared to local statistical filters. In this paper, a coherent impulse and speckle reduction algorithm is proposed which uses a

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combination of local statistics and non-linear Robust Estimator. The method proposes an improvement in local statistics approach for removal of speckle noise. This is followed by application of non linear Robust Estimator, which uses an adaptively increasing localized window of size 11x11 to suppress the impulse noise. The proposed denoising algorithm is evaluated using PSNR and COC as quality metrics. This paper is organized as follows: Section II describes the proposed denoising method. Metrics for evaluation of proposed algorithm and the simulation results are discussed in Section III. Section IV draws the conclusion.

II. PROPOSED DENOISING METHOD The denoising method proposed in this work is a

coherent impulse and speckle reduction algorithm. This uses a combination of local statistics and non-linear Robust Estimator in spatial domain. This is explained under the following heads:

A. Speckle Noise Removal Suppression of speckle noise can be achieved using the

first order local statistics [6]. The contaminated image can be filtered using the following equation: y = m + c(x - m) (1) where: x denotes the input gray level of the noisy pixel, m is the calculated mean of a sliding window of order 3x3 and y is the output gray level of the restored pixel. c is a multiplicative factor [19],[21]-[22] which is a function of local statistics of a sliding window and can be mathematically stated as:

2

2 2 2c=(m . )+

(2)

where: is the variance computed for a sliding 3x3 window and is the speckle noise variance. In the proposed method, the above constant c is calculated using (2), with a modification that: if the value of c evaluates to be greater than 0.01, it is scaled down and substituted equal to 0.01. This poses remarkable improvement in filtering in comparison to the existing method.

B. Impulse Noise Removal

After the removal of speckle from the noisy image, it is made input to the proposed impulse noise removal algorithm. This algorithm processes the input image in two phases. Phase 1: Order Statistics Filtering

The proposed algorithm for impulse noise removal is applied with different (odd) window sizes; starting with an initial window size(w) of 3x3, to a maximum of 11x11 (wmax). Statistical parameters like mean (me), median (md), minimum (min), maximum (max) and standard deviation (std) are computed for the sliding window. An input pixel X(i,j) is considered to be a noise free pixel, if and only if its value lies in between the dynamic range (0,1). Otherwise, it is replaced by a value determined by the procedure explained in the subsequent lines. It is analyzed that if the calculated

value of median (md) from the above window lies between the minimum (min) and the maximum (max) values, then the current pixel is replaced by this median value followed by the application of robust estimator (in Phase-2). Otherwise w is incremented by a factor of 2 (not exceeding wmax) and again the former condition is checked. In case, the new md does not lie between the above limits, w is incremented again (by a factor of 2), iteratively repeating the entire process. If w becomes greater than wmax, then the corrupted pixel should be replaced by the last processed pixel value, skipping the application of robust estimator. In case w expands to 7x7 (not exceeding wmax), the corrupted pixel will be replaced by the last processed pixel value, because for such a large window, the computed median value may also be noisy. This is followed by application of robust estimator as explained in the next phase.

Phase 2: Robust Estimator

Robust Estimator filters draw their mathematical basis from the field of robust statistics. The term ‘robust’ was coined in statistics by G.E.P. Box in 1953 [31]. In general, Robust Estimator is a statistical estimator which is insensitive to small deviations from idealized assumptions for which the estimator is applied [32]-[33]. The technique is based on a simple concept of rejecting the outlier pixels (noise pixels) in the corrupted image that do not belong to the ensemble of samples in an adaptive window around the pixel of interest. The robust estimator function is given as:

2

2

x(x, ) = log(1+ )2

(3)

where: is a scale parameter that controls the outlier rejection.

The influence function is the first derivative of (x, ) with respect to x and can be stated as:

2 2

2x(x, ) =(2 ) + (x )

(4)

Robust Estimation Algorithm is now applied on the output pixel obtained from Phase 1. The local estimate of the image standard deviation N is multiplied by an image

smoothening factor ( ) which lies in the following range: 0.2 ( )≤ ≤ 0.3t o get the maximum expected outlier ( p) as given in (5). p N= . (5)

The scale parameter is calculated by the following equation: p=

2 (6)

Consequently, the difference of each pixel inside the window (size obtained from previous phase) with respect to median (md) is calculated and is used for the calculation of influence function . However, if the above difference comes out to be zero, then the median value of the window is taken into consideration for the influence function determination ( ) (as given in (4)). In case, the md comes out to be zero, then the current pixel is assumed to be at the center of a 3x3

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mask and is convolved with the template given below in (7). The median value of the transformed matrix is then used for the determination of the influence function ( ).

1 1 11H = 1 1 19

1 1 1

(7)

The computed value of the influence function ( ) is now used to determine the estimated value of the pixel which is given by the ratio of S1 and S2 as given in the following equation:

Estimated Pixel Value= 1

2

SS

(8)

where: S1 is given by

1

l= L

pixel(l). (x)S =x

(9)

where, l=L is the number of pixels in the window. S2 is given by:

2

l= L

(x)S =x

(10)

This process is repeated iteratively (again from Phase-1) for the next pixel, till the filtered image is obtained.

III. RESULTS AND DISCUSSION

A. Evaluation of Proposed Method For the assessment of the restored image quality,

quantitative measures are preferred as they can dynamically monitor and adjust image quality, optimize parameter settings and can be used to benchmark digital image processing systems. The quantitative measures used in the paper are: Peak Signal to Noise Ratio (PSNR) and Coefficient of Correlation (COC). The higher the value of PSNR, better is the quality of the restored image. If f(i j) denotes the original image, y(i,j) denotes the restored image, i & j are the pixel position of the M x N image, n is the number of bits, then the Peak Signal to Noise Ratio (PSNR) [34] in dB is given as:

n 2

10(2 -1)PSNR = 10log

MSE (11)

and MSE is given by (12). 2M N

i =1 j=1

1M S E = [f(i, j) - y(i, j)]M .N

(12)

The other quality metric used in this work; Coefficient of Correlation (COC) [35] is given by the following equation:

2 2

(f-f )(y-y)COC=

(f-f) (y-y)

(13)

where: f is the original image, f is the mean of the original image, y is the restored image obtained after the application of proposed denoising algorithm and y is the mean of the restored image. COC as a quality measure evaluates the correlation between the original and the final denoised image by computing the variations in the original pixel value and the final estimated value along with the mean of the two images.

B. Simulation Results The proposed algorithm for denoising an image

contaminated by the noise mixture (speckle + impulse) is tested on a normalized gray scale ‘mandi’ image of size 512 x 512. Speckle and impulse noises are simulated on the input image to perform the experiment. The proposed algorithm is tested on the noise mixture, where the impulse noise varies upto a maximum of 50% intensity and speckle noise variance lies in the range, = 0.01-0.06. Figure 1 (b, d & f) shows denoised images for different intensity combinations of speckle and impulse noise clearly depicting that noise is suppressed very effectively without any blurring. This can be objectively verified by the calculated values of PSNR and COC as shown in Table I. Simulation results indicates significant improvement in the restored image quality in comparison to the other denoising algorithms dealing with individual noise types [36].

IV. CONCLUSION Conventional image denoising algorithms (in spatial

domain) using sliding window approaches for suppression of speckle as well as impulse noise suffer from common limitations like: over smoothening for large window sizes (in case of high noise density) leading to blurred edges, poor filtering for small window sizes, improper choice of threshold leaving the sharp features unprocessed. The denoising approach proposed in this work suggests an improvement in local statistics approach for removal of speckle noise. This is followed by application of non linear Robust Estimator for filtering of impulse noise. In a nutshell it can be concluded that the proposed denoising algorithm suppresses the mixture of speckle and impulse noise along with significant reproduction of local features even for high density contaminations. The efficiency of the proposed algorithm can be visualized from the simulation results and verified by the reasonably high values of the quality metrics (i.e. PSNR and COC). The proposed algorithm is gravely applicable in areas where an already contaminated image is transmitted through a noisy channel.

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= 0

.01

10%

= 0

.03

1

0%

= 0

.05

10%

50%

5

0%

50%

=

0.0

2

10%

=

0.0

4

10%

=

0.0

6

10%

50%

50%

50%

(a) (b) (c) (d) (e) (f)

Fig. 1. Shows the results of the proposed denoising method for different intensity combinations of speckle and impulse noises. (a), (c), (e) Noisy images. (b), (d), (f) Images denoised with the proposed method

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TABLE I. Shows the comparative analysis of obtained PSNR and COC for different combinations of speckle and impulse noise for the proposed denoising algorithm

SPECKLE NOISE

IMPULSE NOISE PSNR(dB) COC SPECKLE

NOISE IMPULSE

NOISE PSNR(dB) COC

= 0.01

10% 34.7807 .9952

= 0.02

10% 33.1145 .9927 20% 34.3643 .9946 20% 32.7245 .9920 30% 33.8445 .9937 30% 32.1987 .9908 40% 33.0340 .9925 40% 31.7770 .9893 50% 32.3491 .9907 50% 31.0250 .9871

= 0.03

10% 31.7277 .9904

= 0.04

10% 30.7860 .9876 20% 31.4271 .9894 20% 30.5354 .9867 30% 31.0310 .9878 30% 30.1370 .9850 40% 30.5423 .9861 40% 29.6575 .9829 50% 29.8678 .9835 50% 29.1314 .9803

= 0.05

10% 29.9636 .9850

= 0.06

10% 29.2204 .9829 20% 29.7391 .9839 20% 28.9187 .9806 30% 29.2718 .9817 30% 28.5770 .9786 40% 28.8354 .9793 40% 28.1598 .9759 50% 28.2615 .9760 50% 27.6248 .9723

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