WEINER FILTER AND SUB-BLOCK DECOMPOSITION BASED IMAGE RESTORATION FOR MEDICAL APPLICATIONS

WEINER FILTER AND SUB-BLOCK DECOMPOSITION BASED IMAGE RESTORATION FOR MEDICAL APPLICATIONS ARIFA SULTANA 1 & KANDARPA KUMAR SARMA 2 1,2 Department of Electronics and Communication Engineering, Gauhati University, Guwahati-781014, Assam, India. E-mail: arifasultana15@gmail.com, kandarpaks@gmail.com Abstract Image restoration is a critical application in image processing where adaptive approaches have continuously provided improved results. The work deals with certain image restoration work using Adaptive Weiner filtering. Initially, we proposed an adaptive image restoration technique based on Weiner filter and certain sub-block decomposition technique which provides improved results for medical images. The work initially performs an adaptive Wiener filtering on certain medical images using the Least Mean Square (LMS) algorithm. This is next compared to a process where a sequence of subblocks are extracted from the image and block-wise adaptive Wiener filtering performed. The results are compared which show that the second approach provides better outcomes. Experimental results demonstrate that higher peak signal to noise ratio (PSNR) values are obtained if the block-sizes are reduced further which, however, contributes towards increased computational complexity. In this paper, we have performed a comparative analysis of the computational time required by the sub-block decomposition technique for a variation in the sub-block size. Keywords- Adaptive Weiner filtering, sub-block decomposition, psnr. I. INTRODUCTION Image restoration is a process imparted in the image using certain objective criteria and prior knowledge so that its visual appearance improves considerably. An image may be degraded because of the modification of the gray values of the individual pixels due to some factors, or it may be distorted because the position of the individual pixels may be shifted away from their correct position [1]. Since present-day imaging technology is not perfect, every recorded image is degraded in some sense. Every imaging system has a limit to its available resolution and the speed at which images can be recorded. Often the problems of finite resolution and speed are not crucial to the applications of the images produced, but there are always cases where this is not so. There exist a large number of possible degradations that an image can suer. Common approaches of image restoration can be divided into two categories: inverse filtering or transform related techniques and algebraic techniques. In Inverse filtering, the techniques involve analysing the degraded image after an appropriate transform has been applied. By acting directly on the transformed image before applying an inverse transform, or using transformed image information to develop an inverse filter, an image may be partially restored. In the Fourier domain, the transfer function of the Inverse filter is the inverse of the degradation function or the distortion applied to the image. This produces a perfect restoration in the absence of noise, but the presence of noise has very bad eects. Since the inverse filtering approach makes no explicit provision for handling noise so the Weiner filtering technique has become very popular. This incorporates both the degradation function and statistical characteristics of noise into the restoration process [2]. Algebraic techniques involve attempts to find a discrete solution to the distortion by matrix inversion techniques or with an iterative method to minimise a degradation measure [3]. Previously, we propose an adaptive image restoration technique based on Weiner filter and certain sub-block decomposition technique which provides improved results for medical images [4]. The work initially performs an adaptive Wiener filtering on certain medical images using the Least Mean Square (LMS) algorithm. This is next compared to a process where a sequence of subblocks are extracted from the image and a block-wise adaptive Wiener filtering performed. The results are compared which show that the second approach provides better outcomes. Experimental results show that higher peak signal to noise ratio (PSNR) values are obtained if the block-sizes are reduced further which, however, contributes towards increased computational complexity. In this paper we have performed a comparative analysis of the computational time required by the sub-block decomposition technique for a variation in the subblock size. II. IMAGE DEGRADATION AND RESTORATION THEORY A. Image degradation model Image degradation process can be modelled as a degradation function together with an additive noise, operates on an input image f (x, y) to produce a degraded image g(x, y) as shown in Figure 1. As a result of the degradation process and addition of noise, the original image becomes 35

Figure 1. Image degradation model. degraded, representing image blur in dierent degrees. If the degradation function h(x, y) is linear and spatially invariant, the degradation process in the spatial domain is expressed as convolution of the f (x, y) and h(x, y), given by g( x, y) f ( x, y) h( x, y) n( x, y) (1) According to the convolution theorem, convolution of two spatial domain functions is denoted by the product of their Fourier transforms in the frequency domain. Thus the degradation process in frequency domain can be written as G F H N (2) [2]. B. Image restoration The objective of image restoration is to reduce the image blur during the imaging process. If prior knowledge of the degradation function is available, the inverse process against degradation can be applied for restoration, including denoising and deconvolution. In frequency domain, the restoration process is given by the expression G N F (3) [4] H III. ADAPTIVE WEINER BASED IMAGE RESTORATION INLCUDING SUB-BLOCK DECOMPOSITION The procedure used in this paper is image restoration using Wiener filter. Wiener filter is a well known filter technique to remove noise and invert the blurring image simultaneously. This technique is quite popular among medical imaging to enhance the quality of images. The concept of Wiener filter is to approximate F (x, y) from non-degraded f(x, y) so that it minimize the mean square error (MSE) between f(x,y) the original image with F(x,y) the estimate restore image. Wiener filter equation was given by * H F G 2 Svv H S (4) where F( u, v ) is estimate of undegraded image, H * ( u, v ) is complex conjugate of H ( u, v ) (degradation function), G is degraded image Svv and is the ratio of the power spectrum S of the noise to the power spectrum of the undegraded image. In order to calculate the estimate of F (u, v), we must know the degradation function H (u, v) or point spread function (PSF) for the image. In this procedure of image restoration, the degradation function was assumed as 2D Gaussian function model. The 2D Gaussian function model can be expressed by 2 2 ( xx0 ) ( y y0 ) [ ] 2 2 2 2 x y f ( x, y) Ae (5) where A is a constant which A > 0 and is the variance [6]. An advantage of Wiener filter is it takes noise eect into consideration for image restoration but the practical problem is that the information about the undegraded image and the noise is not easily available. Some techniques for calculating the point spread function are proposed in [5]. So the significant part of this filter is to find the power spectrum of noise and power spectrum of original image which are Svv ( u, v ) and S ( u, v ) respectively. In this experiment, the estimate ratio of Svv value is treated as constant, so to find the S best value of the constant, try and error technique is used. C. Adaptive Weiner Filter algorithm The adaptive process involves the use of a cost function, which is a criterion for optimum performance of the filter, to feed an algorithm, which determines how to modify filter transfer function to minimize the cost on the next iteration [8]. Weiner filter proves to be a good image restoration technique in the frequency domain but it does not give satisfactory results in the nonstationary environment. So Adaptive Weiner filter is designed using Least Mean Square (LMS) algorithm of the adaptive filters. The conventional LMS algorithm was extended to the 2D case by Hadhoud and Thomas [9]. The steps of the algorithm for adaptive Weiner filtering for a 2-D case maybe summarized as below: 1 Set the step size of the LMS algorithm. 2 Take a very smal value to which the error is to be reduced, say e min =0.000001. 3 Formulate the Weiner filter. Loop: 36

4 Get the estimated image in the frequency domain: Compute the 2D inverse FFT to obtain Figure 3: 2-D image converted into 3 D stack Figure 2: Flowchart for the Adaptive Weiner filter 5. Compute the error e. 6. Update the Weiner filter with 2D LMS weight update equation. 7. Goto step 4 while e>e min. 8: If condition 6 is not met, stop. The flowchart as shown in Figure 2 shows the steps for the above adaptive restoration process. D. Adaptive Weiner Filtering using sub-block decomposition based technique: This proposed technique generates a sequence of sub-blocks from the input image. After this step, block-wise adaptive Wiener filtering is performed. The results are compared which show that this second approach provide better outcomes. The original image of size M by N is divided into smaller blocks each of size M1 by N1. The 2-D image is then converted into a 3D stack form as shown in Figure 3. The above adaptive Weiner filtering is then applied to each block. A restored 2-D image is reconstructed from restored 3-D stack. The flowchart of this proposed technique is shown in Figure 5. III. RESULTS Figure 4: Flowchart for restoration using Adaptive Weiner Filtering applied to constituent subblocks of the image. The results derived are shown for the two separate approaches preferred for the image restoration work proposed in [4]. Here, we have shown a comparative analysis of the computational time required by the sub-block decomposition technique for a variation in the sub-block size. A. Results obtained by the Adaptive Weiner Filter The degraded MRI image is first restored by the Adaptive Weiner Filtering technique. The peak signal to noise ratio (PSNR) of the restored image is calculated for the image quality evaluation. Table I shows the PSNR value of the image restored at the end of every iteration of the process. From the Table I it is clear that the quality of the image is improved at each iteration and the error, i.e. the dierence between the original image and the restored image decreases. This process is repeated till a satisfactory state is reached. Figure 5 shows degraded MRI image and Figure 6 is the restored image obtained after Adaptive Weiner Filtering. The restored image has a PSNR of 20.3951 db. 37

TABLE I. PSNR VALUES OF RESTORED ADAPTIVE WEINER FILTERING IMAGES PRODUCED AT EVERY ITERATION AND THE CORRESPONDING ERROR Iteration Psnr(dB) MSE number 1 20.1317 0.0002542 2 20.1624 0.0002267 3 20.1802 0.0002188 4 20.1823 0.0002022 5 20.2845 0.0002001 6 20.2857 0.0001876 7 20.3922 0.0001688 8 20.3923 0.0001287 9 20.3928 0.0001186 10 20.3931 0.0000723 11 20.3935 0.0000657 12 20.3942 0.0000478 13 20.3946 0.0000277 14 20.3951 0.0000199 A comparison of all restoration performed in this paper is shown in Table III. The sub-block decomposition technique is performed for dierent sub-block sizes and the computational time required for each sub-block size is also calculated. The computational time is provided by Intel Dual-core E6500 processor rated at 2.93 GHz with 2GB RAM. Table IV shows comparative variation of process time for dierent sub-block size. With sub-block decomposition, the adaptive Weiner filtering provides and improvement of 25% compared to the case when the entire image is processed as a singular unit. This is significant. TABLE II. AVERAGE PSNR VALUE OF THE RESTORED IMAGE IN EVERY ITERATION USING THE BLOCKWISE ADAPTIVE WEINER FILTER Iteration Average number psnr(db) of the sub-blocks 1 25.521 2 25.536 3 25.537 4 25.538 5 25.539 6 25.542 7 25.546 8 25.546 9 25.548 10 25.549 Figure 5: Degraded Image Figure 6: Restored image using Adaptive Weiner Filtering with PSNR value 20.3951 db B. Results obtained by the block-wise Adaptive Weiner filter: The original image was of size 225 225 which is decomposed to extract 25 sub-blocks each of size 45 45. The decomposed sub-blocks are processed and the average PSNR value of the sub-blocks at every iteration of the adaptive filtering process is shown in Table II. Table II clearly shows that this technique gives better results compared to the previous one. Figure 7 shows the restored image using this technique. A PSNR value of 25.549 is obtained. The size of the sub-blocks is further reduced to 25 25 and the results show that restored image is improved. Figure 8 shows this image with a PSNR value 31.231. Figure 7: Restored image using Adaptive Weiner Filtering applied to constituent sub-blocks of size 45 45. PSNR value obtained is 25.549dB. Figure 8: Restored image using Adaptive Weiner Filtering applied to constituent sub-blocks of size 25 25. PSNR value obtained is 31.231. 38

TABLE III: COMPARISON OF THE PSNR VALUE USING DIFFERENT TECHNIQUES. Technique used PSNR (db) Adaptive Weiner filter 20.39 Adaptive Weiner Filtering in 25.549 Sub-block of size 45 45 TABLE IV: COMPARISON OF THE PSNR VALUE COMPUTATIONAL TIME REQUIRED USING SUB-BLOCK DECOMPOSITION WITH SUB-BLOCKS OF DIFFERENT SIZE Sub-block size Process time (sec ) Psnr ( db) 75 75 23.87 23.222 45 45 102.45 25.549 25 25 216.56 31.231 Such an improvement is obtained when sub-block size of 45x45 is used. If the sub-block size is improved further, the PSNR value shows a 22% improvement. This is obtained, however, at the expanse of increase in computational complexity by 1.2 times. The increase in computational complexity can be dealt with by better hardware but the proposed method provides a simple and robust framework for image restoration suitable for medical applications. IV. CONCLUSION AND DISCUSSION The work initially performs an adaptive Wiener filtering on a magnetic resonance images using the LMS algorithm. This is next compared to a process where a sequence of sub-blocks is extracted from the image and block-wise adaptive Wiener filtering performed. The results are compared which show that the second approach provides better outcomes. Experimental results show that higher peak signal to noise ratio (PSNR) values are obtained if the blocksizes are reduced further which, however, contributes towards increased computational complexity. From the experimental works it is seen that when the size of the sub-blocks is reduced the image quality is improved, but the computational time is increased. The computational complexity can be reduced by better hardware and improved processing techniques. REFERENCES [1.] M. Petrou and C Petrou: ``Image processing: The Fundamentals, 2 nd ed. John Wiley and sons Ltd, 2010. [2.] R. Gonzalez and R. Woods: ``Digital Image Processing, 3 rd ed., Pearson Education, new Delhi, 2009. [3.] S. Perry: ``Adaptive Image Restoration: Perception Based Neural Network Models and Algorithms, a Ph.D thesis submitted to the School of Electrical and Information Engineering, University of Sydney, Australia,2006. [4.] A. Sultana and K. K. Sarma, Adaptive Image Restoration using Weiner Filter and Sub-Block Decomposition based Technique for Medical Applications, in proceedings of International Conference on Electronics and Communication Engineering, Guwahati, India, pp. 46-50, 2012. [5.] L. Yang, X. Zhang and J. Ren: ``Adaptive Weiner Filtering with Gaussian Fitted point spread function in Image Restoration, IEEE 2 nd International Conference on Software Engineering and Service Science, Beijing, pp. 890-894, July 2011. [6.] M. Hussien, M. Saripan: ``Computed Tomography Soft Tissue Restoration using Weiner Filter, IEEE Student Conference on Research and Development, Malaysia, pp. 415-428, December 2010. [7.] Z. Liu, B. He: ``Adaptive Weiner Filtering formulation on MRI EEG integrated Spatiotemporal Neuroimaging, in Proceedings of IEEE NFSI and ICFBI, Hanzhou, China, pp. 159-161, October 2007. [8.] S. Haykin, T. Kailath: ``Adaptive Filter Theory,4 th ed., Pearson Education, Delhi, 2008. [9.] Hadhoud and Thomas: ``The two dimensional adaptive LMS algorithm, IEEE trans. Circuits syst, vol.35, pp 485-497, May 1988. [10.] A. Jain: ``Fundamentals of Digital Image Processing, Prentice Hall of India, New Delhi, 2008. 39