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 models may not be accurate enough for a faithful reconstruction of the original image. To improve the performance of sparse representation-based image restoration, in this paper the concept of sparse coding noise is introduced, and the goal of image restoration turns to how to suppress the sparse coding noise. To this end, we exploit the image nonlocal self-similarity to obtain good estimates of the sparse coding coefficients of the original image, and then centralize the sparse coding coefficients of the observed image to those estimates. The so-called nonlocally centralized sparse representation (NCSR) model is as simple as the standard sparse representation model, while our extensive experiments on various types of image restoration problems, including denoising, deblurring and super-resolution, validate the generality and state-of-the-art performance of the proposed NCSR algorithm.
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