A SHORT REVIEW ON IMAGE RESTORATION OF NOISY AND BLURRED IMAGES AND COMPARISON OF STATE OF ART ALGORITHMS

: This paper analyzes most of restoration method frequently used and gives comparison of seven recent algorithms in terms of working and applicability It compares algorithms like KSVD, BM3D, CSR, KLLD, SVD based, LPGPCA, NCSR and many other spatial domain, transform domain and dictionary based methods, iterative methods for image restoration of noisy and blurred images. It gives comparative survey of all restoration techniques which will be useful to researchers for further development in the field.


I. INTRODUCTION
Image Restoration is process of regaining the original image from its degraded version [1]. It includes image denoising [28], deblurring, superresolution [1]. It is an ill posed problem and many researchers tried to solve it in various ways. These can be broadly classified and discussed in rest of the paper.

II. CLASSIFICATION OF IMAGE RESTORATION TECHNIQUES
The vast work done in the area can be classified in following heads.  [14]. Block Matching and 3-D Filtering (BM3D) based on variation of K nearest neighbor clustering and 2 stage simplification of EM based estimation of signal variance was developed [16]. Improvements [17] [18] to it are also proposed and used for image restoration. LPGPCA includes 3 steps local pixel grouping, PCA transform and inverse PCA transform [19]. LPGSVD [20] is similar technique to LPGPCA. It also has 3 steps local pixel grouping, SVD computation followed by aggregation.  [33] etc. Using Sparsity property of image many recent methods of Image Restoration [28] are developed such as KSVD [31] [32], Learned Simultaneous Sparse Coding (LSSC) [34], and Clustering-based Sparse Representation (CSR) [35], Non locally Centralized Sparse Representation(NCSR) [1] [36], Clustering-based Denoising with locally learned dictionaries (KLLD) [38] [37]. These are explained below in short.

E. KLLD [38]
This algorithm applies K-means clustering to images. On these clusters PCA transform is applied and then dictionary is formed. It uses steering Kernel Regression for weight calculation [38].

F. CSR [35]
The steps in algorithm are K-means clustering, followed by PCA then shrinkage algorithm. In last step it uses L1 optimization as regularization process. It does not need any initial dictionary.

G. Nonlocally Centralized Sparse Representation (NCSR) [1] [36]
This algorithm is combination of all recent image restoration techniques. It begins with L1 regularization with sparse representation. It improves sparse representation by proposing non locally centralized sparse representation in which image is divided into overlapping patches. It also uses iterative shrinkage algorithm for solving L1 regularized least square problem. It used uses K-means clustering and PCA to form dictionary. To calculate estimation of sparse codes it uses weighted average formula similar to non local means algorithm. It also used maximum a posterior estimation (MAP) for evaluating regularization parameter λ. This algorithm works for denoising, deblurring and super resolution.

H. Direct Regularization
Truncated SVD [26]: SVD [53] [54] solution is given by A= U∑V. If we approximate the SVD solution by considering some rank k matrix is known as truncated SVD solution.

I. Iterative
In iterative algorithms, during the iterations the blurred version of the current restoration result is compared to the recorded image. The difference between the two is scaled and added to the current restoration result to give the next restoration result. Various iterative algorithms are Van Cittert Algorithm [39] [40], Landweber Algorithm [39] [41] [42] [43], Poisson Map Algorithm [39], Richardson-Lucy Algorithm [39], Iterative Shrinkage Thresholding algorithm (ISTA) [44], Fast Iterative Shrinkage Thresholding algorithm (FISTA) [45] [46], Two step Iterative Shrinkage Thresholding algorithm (TwIST) [47]. ISTA [44] implements Landweber algorithm followed by soft thresholding [8] for restoration. FISTA [45] [46] is same as ISTA except that iterative shrinkage step considers two previous points for calculation instead of one point. TwIST [47] combines advantages of two methods ISTA and Iterative Re-weighted Shrinkage (IRS) [55] [56] algorithm. It gives good denoising performance as IST algorithm and speed as IRS algorithm.

J. Expectation Minimization (EM) [48] algorithm
The Expectation Minimization (EM) [48] algorithm is a general procedure for finding maximum likelihood parameter estimates. It consists of two steps Expectation step and Maximization step. By alternating the E-step and the M-step, convergence to an optimum of the likelihood function is achieved.

L. Fusion:
Fusion of two or more restored images can be done to improve quality of restored image. Wavelet based fusion of two restored images by two different algorithms like Lucy Richardson, Wiener are used in [51] [52]. Table I compares state of art algorithms and illustrates that all of them use as basic steps pixel grouping or clustering followed by PCA or SVD as decomposition method.

III. CONCLUSION
This paper compared many restoration techniques and analyzed based on working and applicability. Out ofall the algorithms discussedmaximum basic filters and above compared algorithms in table 1 work for image denoising. For image deblurring inverse filter and all iterative techniques are used dominantly in literature but it can also be done by direct methods. NCSR gives results for denoising, deblurring and super resolution.