RESOLUTION ENHANCEMENT TECHNIQUE FOR NOISY MEDICAL IMAGES

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1 International Journal of Electronics and Communication Engineering & Technology (IJECET) Volume 6, Issue 10, Oct 2015, pp , Article ID: IJECET_06_10_002 Available online at ISSN Print: and ISSN Online: IAEME Publication RESOLUTION ENHANCEMENT TECHNIQUE FOR NOISY MEDICAL IMAGES Jesna K H PG scholar, Department of ECE, Ilahia College of Engineering and Technology, Muvattupuzha, Ernakulam ABSTRACT The objective of this paper is to estimate a high resolution medical image from a single noisy low resolution image with the help of given database of high and low resolution image patch pairs. Initially a total variation (TV) method which helps in removing noise effectively while preserving edge information is adopted. Further denoising and super resolution is performed on every image patch. For each TV denoised low-resolution patch, its highresolution version is estimated based on finding a nonnegative sparse linear representation of the TV denoised patch over the low-resolution patches from the database, where the coefficients of the representation strongly depend on the similarity between the TV denoised patch and the sample patches in the database. The problem of finding the nonnegative sparse linear representation is modeled as a nonnegative quadratic programming problem. The proposed method is especially useful for the case of noise-corrupted and low-resolution image. Key words: Single Image Super Resolution, TV Denoising, Medical Imaging, Sparse Representation. Cite this Article: Jesna K H. Resolution Enhancement Technique for Noisy Medical Images, International Journal of Electronics and Communication Engineering & Technology, 6(10), 2015, pp INTRODUCTION In medical imaging, images are obtained for medical purposes, providing information about the anatomy, the physiologic and metabolic activities of the volume below the skin. The arrival of digital medical imaging technologies such as Computerized Tomography (CT), Positron Emission Tomography (PET), Magnetic Resonance Imaging (MRI), as well as combined modalities, e.g. SPECT/CT has revolutionized modern medicine. But due to imaging environments it is not easy to obtain an image 6 editor@iaeme.com

2 Resolution Enhancement Technique For Noisy Medical Images at a desired resolution. Presence of noise may reduce adversely the contrast and the visibility of details that could contain vital information, thus compromising the accuracy and the reliability of pathological diagnosis. Thus resolution improvement became necessary. SR methods can be broadly categorized into two main groups: multi-image SR and single-image SR. In multi-image super resolution techniques as its name implies it uses multiple LR images of the same scene for the reconstruction of HR image. This technique involves three sub-tasks: registration, fusion and deblurring. The first and most important task of these methods is motion estimation or registration between LR images because the precision of the estimation is crucial for the success of the whole method. However, it is difficult to accurately estimate motions between multiple blurred and noisy LR images in applications involving complex movements. This is the reason why multi-image based SR methods are not ready for practical applications. The single-image SR methods, also known as example learning- based methods, emerged as an efficient solution to the spatial resolution enhancement problem. An advantage of these methods over multi-image based SR is that they do not require many LR images of the same scene as well as registration. In single-image SR methods, an image is considered as a set of image patches and SR is performed on each patch. As its name implies, the focus of single-image super resolution is to estimate a high-resolution (HR) image with just a single low-resolution image, and missing high frequency details are recovered based on learning the mapping between low and high-resolution (HR) image patches from a database constructed from examples. Many single-image based SR have been proposed, some of them are based on nearest neighbour search [5] and others are based on sparse coding [6]. In nearest neighbor search methods, each patch of the LR image is compared to the LR patches stored in the database in order to extract the nearest LR patches and hence the corresponding HR patches. These HR patches are then used to estimate the output via different schemes. One of the issues of the single-image based super-resolution is that it highly depends on the database of low and high-resolution patch pairs. However, in medical imaging, we observe the interesting fact that many images were acquired at approximately the same location. Thus, we can collect similar (same organ, same modality) and good quality (proven by experts) images and use them as examples to establish a database of low and high resolution image patch pairs. Another challenge is the questionable performance of these methods when dealing with noisy images. Most of super-resolution algorithms assume that the input images are free of noise. Such assumption is not likely to be satisfied in real applications such as medical imaging. To deal with noisy data, many existing methods proposed two disjoint steps: first denoising and then super resolution. The proposed system is developed in such a way to increase the robustness to noise. Every noisy input image is initially denoised using total variation algorithm, then we estimate its HR version as a sparse positive linear combination of the HR patches in the database with two conditions: (i) the HR estimated version should be consistent with the TV denoised LR patch under consideration, and (ii) the coefficients of the sparse positive linear combination must depend on the similarity between the TV denoised LR patch and the example LR patches in the database. The proposed SR method has some advantages as follows: 7 editor@iaeme.com

3 Jesna K H It can be applied even if the input LR image is a noiseless image or a noisy one. Compared with the nearest neighbors-based methods, the proposed sparsity-based method is not limited by the choice of the number of nearest neighbors. Unlike the conventional SR methods via sparse representation, the proposed method efficiently exploits the similarity between image patches, and does not train any dictionary. 2. EXISTING METHOD Now let us recall the problem of resolution enhancement technique. Assume that we are given a set of example images (high quality images) and a LR image Y generated from the original HR image X by the model, Y = D s HX + η, (1) where H is the blur operator, Ds is the decimation operator with factor s, and η is the additive noise component. The SR reconstruction problem is to estimate the underlying HR version X of Y. In the example-based SR methods, an image is considered as an arranged set of image patches and the super-resolution is performed on each patch. Conventionally, a single image SR method consists of two main phases: database construction and super-resolution. In the first phase, a set of LR and HR image patch pairs is first extracted from the example images. Then, the database, denoted by vector pairs are defined as, (2) = F l p l and = F h p h (3) where F l, F h are the operators extracting the features of the LR and HR patches such as edge information, contours, first and second-order derivatives. In the superresolution phase, a set of feature vectors of image patches is first extracted from the LR input image Y, in a similar way as P l. Then, the missing high frequency components in the corresponding HR patches of the HR output image X are estimated based on the co-occurrence relationship between vector pairs in the database (P l, P h ). In this section, we will briefly present the Novel example based SR method [1], which is related to our work. (A) Novel Example Based SR Method In this technique Denoising and super-resolution is performed on every image patch. For each low-resolution input patch, its high resolution version is estimated based on finding a nonnegative sparse linear representation of the input patch over the low resolution patches from the database [5]. Once the sparse coefficient is obtained denoised LR patches and HR patches can be obtained just by multiplying the sparse coefficient by database of LR and HR patches as denoted below. The LR patches can be obtained as, The HR patches can be obtained as, (4) (5) 8 editor@iaeme.com

4 Resolution Enhancement Technique For Noisy Medical Images Where is the sparse non-negative coefficient, and represents the LR and HR patches. Then the LR and HR patches are placed in proper locations of LR and HR grids and overlapping regions are averaged to obtain the LR and HR images. These two images are combined using IBP algorithm [9] inorder to obtain output super resolution image. The disadvantage of this technique is that in the presence of very high noise the resolution enhancement is poor. Thus both the existing methods fail in the presence of very high noise. 3. THE PROPOSED METHOD The basic idea of the proposed technique is to denoise the input noisy LR image using Total Variational (TV) algorithm and then a sparse weight model is introduced. This model is an integrated framework of super-resolution and denoising, providing us both super-resolved and denoised solutions. This method is very suitable for medical images since these images are often affected not only by limited spatial resolution but also by noise, making the structures or objects of interest indistinguishable. This method can improve the detection by enhancing the spatial resolution while removing noise. The basic idea is to find a non-negative sparse representation of the denoised LR image over the training database P l. We benefit from the advantages of both the existing methods. Before presenting the proposed method in details, let us begin by recalling the image degradation model. Assume that we obtained a LR image Y which contain less amount of noise after denoising by TV algorithm, generated from a HR image X by the model (1). Without loss of generality, the image s values in this work are assumed to be positive. Our aim is to estimate the unknown HR image X from Y with the help of a given set of standard images {A h } which are used as examples. The LR image Y will be represented as a set of N overlapping image patches, that is Y = { y l i, i = 1, 2,..., N}, (6) where y l i is a image patch and N is the number of patches generated from the image Y. Note that N depends on the patch size and the sliding distance between adjacent patches. Similarly, the high-resolution image X can be also represented as a set of the same number N of paired HR patches {x h i, i = 1, 2,..., N}. The size of x h i is set to be where. The LR patch and the HR patches are related by y l i = D s H x h i + η i (7) where η i is the noise in the i th patch. For the sake of simplicity, we assume that the noise, η i N(0, σ i 2 ) (8) is Gaussian, white, zero-mean, and i.i.d., with variance σ i 2. Thus, we can consider y l i as a LR version of the HR patches x h i. In the remaining of this paper, image patches are rearranged as vectors, for example, x h i є R n and y l i є R m. Hereafter, an image patch also designates its corresponding vector. In order to estimate X, the proposed algorithm is also performed in three phases: database construction phase, denoising using TV algorithm and super-resolution reconstruction phase: In the first phase, a database of HR and LR patch pairs (P l, P h ) = {(u l k, u h k ), k є I} where I is the index set, is constructed from a given set of the example images (standard images taken at nearly the same locations as the LR image Y). 9 editor@iaeme.com

5 Jesna K H Second phase is the denoising phase which utilizes Total Variational (TV) algorithm. The super-resolution reconstruction phase consists of the HR patch reconstruction. In order to obtain a good database, the selection of these example images should be such that they would contain a variety of intensities as well as shapes and very little noise. Since the standard images and the LR image are often taken from nearby locations and thanks to the repetition of local structures of images, small image patches tend to recur many times inside these images. Thereby, we can assume that for a given LR image patch in Y, a large number of similar patches can be extracted from the database. (A) Database construction phase In this work, the database of patch pairs is constructed in a simple manner as follows. From the example images, a set {p h k, k є I} of vectorized image patches of size n n is first extracted. Then, for each p h k, a corresponding vectorized patch p l k є R m is determined by, p l k = D s H p h k (8) We consider p h k as a HR patch and p l k as the corresponding LR version. Note that, the LR patch p l k is considered as noise-free one. Consequently, we obtain a database of high-resolution/ low-resolution patch pairs, We denote below the training set as, (P l, P h ) = { є R m R n, k є I } (10) Here five images are considered CT image of abdomen of size, CT image of thorax of size, CT image of chest, MRI image of ankle, and MRI image of knee as shown in Fig 1. (B) Denoising using TV algorithm The total variational technique [2] has advantages over the traditional denoising methods such as linear smoothing, median filtering, Transform domain methods using Fast Fourier transform and Discrete Cosine Transform which will reduce the noise in medical images but also introduce certain amount of blur in the process of denoising which will damage the texture in the images in lesser or greater extent. The Total Variational approach will remove the noise present in flat regions by simultaneously preserving the edges in the medical images which are very important in diagnostic stage. The total variation (TV) of a signal measures how much the signal changes between signal values. Specifically, the total variation of an N-point signal x(n),1 n N is defined as, (11) Given an input signal x n, the aim of total variation method is to find an approximation signal call it, y n, which is having smaller total variation than x n but is "close" to x n. One of the measures of closeness is the sum of square errors: (9) 10 editor@iaeme.com

6 Resolution Enhancement Technique For Noisy Medical Images So the total variation approach achieves the denoising by minimizing the following discrete functional over the signal y n : E x, yv y By differentiating the above functional with respect to y n, in the original approach we will derive a corresponding Euler-Lagrange equation which is numerically integrated with x n (the original signal) as initial condition. Since this problem is a convex functional, we can use the convex optimization techniques to minimize it to find the solution y n. The problem of image denoising or noise removal is, given a noisy image G, to estimate the clean underlying image Y. For Gaussian noise (additive white), the degradation model describing the relationship between G(x, y) and Y(x, y) is G (x, y) = Y (x, y) + (x, y) (14) Where (x, y) is i.i.d zero mean Gaussian distributed. Getting the good denoising results depend on using a good noise model which will accurately describe the noise in the given image. The noise model for Gaussian noise can be given as Where 1/Y is the normalization such that densities sum to one. (12) (15) Figure 1 Test HR images (a) CT image of abdomen (b) CT image of thorax (c) CT image of chest (d) MRI image of ankle (e) MRI image of knee A General model for TV-regularized denoising, Deblurring, and Inpainting is to find an image Y ( x, y) that minimizes: Where denotes the gradient, 2 denotes Laplacian, and ǁ.ǁ p denotes the L p norm on W. Variable (x, y) will be used to denote a point in two-dimensional space. Y (x, y) is an original image, G (x, y) is an observed noisy image. The integrals are over a twodimensional bounded set and denotes the gradient magnitude of Y (x, y). Function G(x, y) is the given noise and blur corrupted image, K is the blur operator, λ( x, y) is a nonnegative function specifying the regularization strength, BV stands for Bounded variation and F determines the type of data fidelity: (16) (17) 11 editor@iaeme.com

7 Jesna K H For simplicity, x, yis usually specified as a positive constant, x=in the denoising process the regularization parameter is having a critical role. The denoising is zero when = 0, therefore the result is same as the input signal. As the regularization parameter increases the amount of denoising is also increases, when the total variation term plays strong role, which will produce the smaller total variation, at the expense of being less like the input (noisy) signal. So the regularization parameter choice is critical for achieving the right amount of noise removal. The Total variation approach is to search over all possible functions to find a function that minimizes (16). Here split Bregman method is used to solve the minimization problem by operator splitting and then solving split problem by applying Bregman iteration [10]. For (16), the split problem is (18) The split problem is not different from the original (16). The point is that the two terms of the objective have been split: The first term only depends on and the second term only on z. Still and z are indirectly related through the constraints = f, z = KY. Now the Bregman iteration is used to solve the split problem. In every iteration, it calls for the solution of the following problem: ( Additional terms in the above expression are quadratic penalties enforcing the constraints and b 1, b 2 are the variables connected to the Bregman iteration algorithm [10]. The solution of (19), which minimizes jointly over,, z, Y is approximated by alternatingly minimizing one variable at a time, that is, fixing z and Y minimising over then fixing and Y minimising over z and so on. This method leads to three variable subproblems: 1. The subproblem: Variables z and Y are fixed and the sub problem is, (19) Its solution decouples over x and is known in closed form: (20) (21) 2. The z subproblem: Variables and Y are fixed and the sub problem is, The solution decouples over x. The optimal z satisfies, (22) (23) 12 editor@iaeme.com

8 Resolution Enhancement Technique For Noisy Medical Images 3. The Y subproblem: Variables and z are fixed and the sub problem is, (24) For denoising K is identity and the optimal Y satisfies, (25) The overall Total Variational (TV) algorithm is as follows. Total Variational (TV) Algorithm: Initialize Y = z = b 2 = 0, While not converged" Solve the sub problem Solve the z sub problem Solve the Y sub problem and While solving these subproblems, the x th sub problem solution is computed from the current values of all other variables and overwrites the previous value of variable x. Convergence will be checked by testing the maximum difference from the previous iterate:. (C) Patch Super Resolution In this phase, the sparse weight optimization model is proposed for super-resolution and denoising on image patch. The optimization problem is established such that its solution determines a non-negative sparse linear representation of the input LR patch over the example patches in the database, and a measure of similarity between patches is proposed and used as penalization function to enforce sparsity. Let us consider an LR patch y l i = D s H x h i + η i with the noise component η i N (0, σ i 2 ). The problem is to find an estimate of the HR patch x h i, from y l i with the help of the database (P l, P h ). Thanks to the repetition of local structures of images, we can expect that there exists a subset of patches u h k P h which have similar structures as those in x h i. Such patches will play an important role in determining the estimate of x h i.. In this work, it is assumed that x h i R n can be represented as a sparse non-negative linear combination of the HR patches in P h, (26) where the vector of representation coefficients α i = [α i1, α i2,...,α ik,...] T 0. Note that unlike the previous ScSR methods here we use non-negative constraint on the coefficients α ik. This can be explained by considering both sides of equation. Due to the fact that the vectors x h i and u h k are defined from the pixel values of image patches, they are then positive vectors. Thus, in the equation x h i = P h α i, both x h i and P h are non-negative. This is why we can require the non-negative constraint on α i Now, consider the corresponding LR patch y l j of x h i. Since it is assumed that x h i = P h α i, multiplying this equation by D s H gives, D s H x h i = D s H P h α i = P l α i (27) 13 editor@iaeme.com

9 Jesna K H By exploiting the relation between the LR and the HR patches, we obtain, (28) whereξ i is related to the noise power σ i of η i. As it can be seen, the LR patch y l i can be represented by the same sparse vector α i over the database of LR patches P l, with a controlled error ξ i. This implies that for a given LR patch y l i, the estimate of the corresponding HR patch x h i is performed by first determining sparse representation vector α i of y l i with respect to the database of LR patches P l. Then, x h i can be h recovered by simply multiplying this representation by the database P h, i = P h α i. This is the core idea behind the proposed method. More precisely, our aim is to find the patches u h k which should be similar to x h i and then to use them for the estimation of x h i. Therefore, in order to select the similar patches (in the database) with x h i, we try to force coefficient vector α i =[α i1, α i2,...,α ik,...] T such that most of its zero components, α ik, correspond to the elements u h k which are dissimilar to x h i. The problem of finding the vector α i can be given as: (29) Subject to where α =[α i1, α i2,...,α ik,...] T, is a given positive number, σi is the standard deviation of the noise in the ith patch, the l 0 -norm assures that the solution α i is a sparse one, while the positive penalty coefficients w ik depend on the dissimilarity (or inversely the similarity) between denoised LR patches and LR patches in the database. Generally we force small values for α ik for high dissimilarity or for weak similarity. Dissimilarity is estimated using denoised LR patches and LR patches in the database since HR patches are not available initially. The penalty coefficients w ik is defined as, (30) Where d is the criterion determining the similarity between y l i and u l k, while is a non-negative increasing function. Normally, to measure the extent of dissimilarity among the image patches, one of the most popular dissimilarity criteria is the Euclidian distance. However, in this case y l i is a vector defined from the pixel values of the i th patch of the input LR image Y while u l k is a normalized example vector in the database. Moreover, y l i is also corrupted by noise η i. Thus, using the Euclidian distance may not be effective enough. To obtain a better dissimilarity criterion, let us consider the relationship of y l i and u l k. Now let us with definition of congruence of image patches. Two image patches x 1 and x 2 are congruent if there exists a non-zero constant μ R, with x 1 = μx 2. As already mentioned y l i is corrupted by Gaussian white noise η i N(0, σ 2 i ) with y l i = D s H x h i + η i. Thus, the patch u l k is ideally similar to y l i if u l k is congruent to D s H x h i. That means there exists a constant μ ik > 0 such that, (31) According to the assumption for the noise component η i N(0, σ i 2 ) the mean of η i, E(η i ) 0. Therefore the constant μ ik can be approximated as, 14 editor@iaeme.com

10 Resolution Enhancement Technique For Noisy Medical Images (32) Thus we can write, (33) Therefore, we propose to use the parameter a ik such that, The parameter a ik allows us to evaluate the statistical property of noise in the residual patch. So, in this work, the dissimilarity criterion d is defined by, (34) Here i (. ) is defined as i (t)=t if σ i =0 otherwise, if σ i > 0 then, (35) Where ρ i is a positive threshold depending on y l i. As can be seen, the function i (t) strongly increases when t >ρ i. In other words, the penalty coefficients corresponding to the example patches such that > ρ i will be very high. Note that in the ideal case, we have, Where m is the number of elements in vector y l i, and is a positive constant. The threshold ρ i in (36) is set to γ(mσ 2 i ). l 0 -norm is not a true norm thus the problem (29) is too complex to solve in general. To avoid the above problem we replace l 0 -norm by l 1 -norm, and problem (29) becomes convex and can be rewritten as: (36) (37) (38) Subject to which is equivalent to, (39) subject to Lagrange multipliers allow an equivalent formulation, Where the parameter λ balances sparsity of the solution and fidelity of the approximation to y l i. The computation time can be reduced by imposing a threshold on the dissimilarity criterion d. Let us denote S(y l i) = {k I:α ik > 0} as the support set of y l i. As analyzed above, S(y l i) involves u l k where d(y l i, u l k) is not very large. Thus, with a suitable value of the threshold r i, there exists a subset I i of I, (40) 15 editor@iaeme.com

11 Jesna K H (41) Such that (42) Thus, inorder to save computing time, problem (40) should be considered on the subset I i, Easily can be rewritten as, (43) Where U i is the matrix whose columns are the vectors u l k, w i is the vector formed by concatenating all the coefficients λ(1+w ik ), here k I i. It can be seen that the problem (44) is a non-negative quadratic programming (NQP). It can be solved by using multiplicative updates algorithm proposed by Hoyer. The algorithm is as follows. Multiplicative updates algorithm for NQP: Input: α =α 0 > 0, number of iterations T Updating: t=0 While t < T & =.*( )./( + ) ; t = t + 1; End Output: Once is obtained the desired HR and LR patch can be obtained by just multiplying with the database of HR and LR patches. The HR patches can be obtained as, (44) The LR patches can be obtained in the same manner, (45) (46) (a) (b) Figure 2 Results on MRI image of ankle (a) Result of the proposed method (b) Original test image editor@iaeme.com

12 Resolution Enhancement Technique For Noisy Medical Images (D) Reconstruction of the Entire HR Image To obtain the entire HR image, we first set all the estimated HR patches in the proper locations in the HR grid. A coarse estimate of X, is then computed by averaging in overlapping regions. In the same way, we obtain a denoised image, denoted by Y denoise of Y by replacing the noisy patches by the denoised ones, and then performing averaging in overlapping regions. Final HR image is determined as a minimizer of the following problem. The iterative back-projection (IBP) algorithm [9] is used to solve this problem, Where X t is the estimate of the HR image at the t-th iteration denotes the upscaling by factor s and p is a Gaussian symmetric filter. The result obtained by using this technique is as shown in figure 2. The overall algorithm for resolution enhancement is as follows: INPUT: The LR image Y and the size of LR patch. Magnification factor s. Database (P l, P h ) = {(u k l, u k h ), k I}. Regularization parameter λ, number T of iterations. OUTPUT: HR image BEGIN 1. Denoise the input image using Total TV algorithm. 2. Partition Y into an arranged set of N overlapping patches. 3. For each patch of Y Compute the dissimilarity criteria d( ). Determine the subset I i. If > 0, compute the penalty coefficients W i. Find α using multiplicative updates algorithm. Generate the HR patch and the denoised LR patch. 4. END 5. FUSION: Produce the initial HR image and the denoised image. 6. IBP enhancement: using the IBP procedure find the final HR image. END 4. PERFORMANCE EVALUTION In order to evaluate the objective quality of the super- resolved images, we use two quality metrics, namely Peak Signal to Noise Ratio (PSNR) and Structural SIMilarity (SSIM). The PSNR measures the intensity difference between two images. However, it is well-known that it can fail to describe the subjective quality of the image. SSIM (47) (48) 17 editor@iaeme.com

13 Jesna K H is one of the most frequently used metrics for image quality assessment. Compared with PSNR, SSIM better expresses the structure similarity between the recovered image and the reference one. Here we consider novel example based SR technique for the comparison of result. For novel example based SR PSNR was obtained as and SSIM as 0.43, whereas for the proposed techniques PSNR I is obtained as and SSIM as CONCLUSION In this paper, we proposed an effective super resolution technique for resolution enhancement which is very robust to heavy noise. The technique relies on the interesting idea that consists of using standard images to enhance the spatial resolution while denoising the given degraded and low-resolution image using Total Variational (TV) algorithm. Since medical images are specific, using this specificity for performing super-resolution allows more efficient solution than a conventional SR method. Experiment results show the effectiveness of the proposed technique and thereby demonstrating the ability of the technique for the potential improvement of diagnosis accuracy. ACKNOWLEDGMENT First of all I thank and praise the Almighty, without whom nothing is possible, for the spiritual support, eternal guidance and all blessings. And now I express my sincere gratitude to Asst Prof. ANGEL P MATHEW, project coordinator, and Asst Prof. RASEENA K A, project guide, for their encouraging status and timely help which have constantly stimulated me to travel eventually towards the completion of my project. REFERENCES [1] D. H. Trinh, M. Luong, F. Dibos, J. M. Rocchisani, C. D. Pham, and T. Q. Nguyen, Novel Example-Based Method for Super-Resolution and Denoising of Medical Images, IEEE Image Processing, Vol. 23, No. 4, April [2] V N Prudhvi Raj and Dr T Venkateswarlu Denoising Of Medical Images Using Total Variational Method Signal & Image Processing : An International Journal (SIPIJ) Vol.3, No.2, April [3] S. C. Park, M. K. Park, and M. G. Kang, Super-resolution image reconstruction: A technical overview, IEEE Signal Process. Mag., vol. 20, no. 3, pp , May [4] W. T. Freeman, T. R. Jones, and E. C. Pasztor, Example-based super resolution, IEEE Comput. Graph. Appl., vol. 22, no. 2, pp , Apr [5] H. Chang, D. Yeung, and Y. Xiong, Super-resolution through neighbor embedding, in Proc. IEEE CVPR, Jul. 2004, pp [6] J. Yang, J. Wright, T. Huang, and Y. Ma, Image super-resolution as sparse representation of raw image patches, in Proc. IEEE CVPR, Jun. 2008, pp [7] J. Wang, S. Zhu, and Y. Gong, Resolution enhancement based on learning the sparse association of image patches, Pattern Recognit. Lett., vol. 31, no. 1, pp. 1 10, [8] J. Yang, J. Wright, T. Huang, and Y. Ma, Image super-resolution as sparse representation of raw image patches, in Proc. IEEE CVPR, Jun. 2008, pp editor@iaeme.com

14 Resolution Enhancement Technique For Noisy Medical Images [9] M. Irani and S. Peleg, Motion analysis for image enhancement: Reso-lution, occlusion and transparency, J. Vis. Commun. Image Represent, vol. 4, no. 4, pp , Dec [10] Wotao Yin, Stanley Osher, Donald Goldfarb And Jerome Durbon, Bregman Iterative Algorithms for Minimization with Applications to Compressed Sensing, vol. 1,No.1, pp [11] Mayuri Y. Thorat and Vinayak K. Hybrid Method To Compress Slices of 3d Medical Images, International Journal of Electronics and Communication Engineering & Technology, 4(2), 2013, pp