A Novel Sparse Representation Method for Image Restoration Applications

Sparse representation has been widely used in various image restoration applications. The quality of image restoration mainly depends on whether the used sparse domain can represent well the underlying image. Since the contents representing the underlying image can vary significantly across different images or different patches in an image, we propose to learn various sets of bases from a precollected dataset of example image patches and for processing a particular given patch, a suitable set of base is selected adaptively as local sparse domain. Here we introduce two adaptive regularization terms into the sparse representation framework. One is a set of auto regressive (AR) models are learned from the pre-collected dataset of example image patches and the best fitted AR model is adaptively selected for regularization. Second is image non-local self similarity regularization to regularize the image local structures. To make the sparse coding more accurate, a centralized sparsity constraint is introduced by exploiting the nonlocal image statistics. The local sparsity and the nonlocal sparsity constraints are unified into a variational framework for optimization. Extensive experiments on the proposed method of CSR method achieves convincing improvement over previous state-of-the-art methods in terms of PSNR and SSIM values. Keywords--------Image restoration, deblurring, superresolution, sparse representation, regularization INTRODUCTION Image restoration (IR) aims to recover a high-quality image from its degraded (e.g., noisy, blurred and/or downsampled) versions, which may be taken, for example, by a low-end camera and/or under limited conditions. For an observed image Y, the problem of IR can be expressed by v DHX Y + = . (1) where X is the unknown image to be estimated, and H and Dare degrading operators and υ is additive noise. When H and D are identities, the IR problem becomes denoising; when D is identity and H is a blurring operator, IR becomes deblurring; when D is identity and H is a set of random projections, IR becomes compressed sensing[3]; when D is a down-sampling operator and H is a blurring operator, IR becomes (single-image) super-resolution. IR, a fundamental problem in image processing has been widely studied in the past three decades.In this paper, we focus on deblurring and single-image super-resolution. Due to the ill-posed nature of IR[2], the solution to (1) with an l2-norm fidelity constraint, i.e., 2 2 min arg ˆ DHX Y X X − = . is generally not unique. A prior knowledge of natural images can be used to regularize the IR problem for finding a better solution. One of the most commonly used regularization models is the total variation (TV) model } . 2 2 min{ arg ˆ 1 X DHX Y X X ∇ + − = λ , where 1 X ∇ is the l1-norm of the first-order derivative of X and λ is a constant. The success of TV regularization validates the importance of good image prior models in solving the IR problems. In wavelet based image denoising the sparsity of wavelet coefficients can serve as good prior. This reveals the fact that many types of signals, e.g., natural images, can be sparsely represented (or coded) using a dictionary of atoms, such as DCT or wavelet bases, that is, denoting by Φ the dictionary, we have α Φ ≈ X and most of the coefficients in α are close to zero. With the sparsity prior, the representation of X over Φ can be estimated from its observation Y by solving the following l0-minimization problem: } . 2 2 min{ arg ˆ 0 α λ α α α + Φ − = DH Y , where the l0-norm counts the number of nonzero coefficients in vector α . Once we obtainα̂ , X can then be estimated as α̂ Φ = X  . The l0–minimization is an NPhard combinatorial search problem, and is usually solved by greedy algorithms. The l1-minimization, as the closest convex function to l0-minimization, is then widely used as an alternative approach to solving the sparse coding problem: } . 2 2 min{ arg ˆ 1 α λ α α α + Φ − = DH Y . For better IR results the l1 –norm sparsity regularization term has been iteratively reweighted. Sparse representation has been successfully used in various image processing applications. The main issue in sparse representation modeling is the determination of dictionary Φ . Many dictionary learning (DL) methods aim at learning a universal and overcomplete dictionary to represent various image structures. However, sparse decomposition over a highly redundant IJCSET |September 2012 | Vol 2, Issue 9, 1386-1395 www.ijcset. net | ISSN:2231-0711