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Sparse representation models code an image patch as a linear combination of a few atoms chosen out from an over-complete dictionary, and they have shown promising results in various image restoration applications. However, due to the degradation of the observed image (e.g., noisy, blurred, and/or down-sampled), the sparse representations by conventional(More)
As a powerful statistical image modeling technique, sparse representation has been successfully used in various image restoration applications. The success of sparse representation owes to the development of the <i>l</i><sub>1</sub>-norm optimization techniques and the fact that natural images are intrinsically sparse in some domains. The image restoration(More)
Simultaneous sparse coding (SSC) or nonlocal image representation has shown great potential in various low-level vision tasks, leading to several state-of-the-art image restoration techniques, including BM3D and LSSC. However, it still lacks a physically plausible explanation about why SSC is a better model than conventional sparse coding for the class of(More)
This paper presents an efficient image denoising scheme by using principal component analysis (PCA) with local pixel grouping (LPG). For a better preservation of image local structures, a pixel and its nearest neighbors are modeled as a vector variable, whose training samples are selected from the local window by using block matching based LPG. Such an LPG(More)
Where does the sparsity in image signals come from? Local and nonlocal image models have supplied complementary views toward the regularity in natural images-the former attempts to construct or learn a dictionary of basis functions that promotes the sparsity; while the latter connects the sparsity with the self-similarity of the image source by clustering.(More)
Sparse representation is proven to be a promising approach to image super-resolution, where the low-resolution (LR) image is usually modeled as the down-sampled version of its high-resolution (HR) counterpart after blurring. When the blurring kernel is the Dirac delta function, i.e., the LR image is directly down-sampled from its HR counterpart without(More)
Sparsity has been widely exploited for exact reconstruction of a signal from a small number of random measurements. Recent advances have suggested that structured or group sparsity often leads to more powerful signal reconstruction techniques in various compressed sensing (CS) studies. In this paper, we propose a nonlocal low-rank regularization (NLR)(More)
This paper presents a novel non-local iterative back-projection (NLIBP) algorithm for image enlargement. The iterative back-projection (IBP) technique iteratively reconstructs a high resolution (HR) image from its blurred and downsampled low resolution (LR) counterpart. However, the conventional IBP methods often produce many &#x201C;jaggy&#x201D; and(More)
The reconstruction of a high resolution (HR) image from its low resolution (LR) counterpart is a challenging problem. The recently developed sparse representation (SR) techniques provide new solutions to this inverse problem by introducing the l 1-norm sparsity prior into the super-resolution reconstruction process. In this paper, we present a new SR based(More)
This paper proposes a novel sparse representation model called centralized sparse representation (CSR) for image restoration tasks. In order for faithful image reconstruction, it is expected that the sparse coding coefficients of the degraded image should be as close as possible to those of the unknown original image with the given dictionary. However,(More)