Image restoration using structured sparse representation with a novel parametric data-adaptive transformation matrix

In this paper, we propose a new framework for image restoration by combining nonlocal regularization technique with structured sparse representation using a novel parametric data-adaptive transformation matrix. Specifically, we first present a parametric nonlocal difference operator in the context of nonlocal regularization with the insight that the weight functions in the definition of the nonlocal difference operator play an important role in modeling image prior information. The proposed difference operator not only gives flexibility in modeling prior knowledge of clean images compared with the conventional methods, but also leads to a novel parametric data-adaptive transformation matrix. Then, we propose a structured sparse representation model based on this new transformation matrix for image restoration, taking advantage of the sparse nature of the transform coefficients of image patches over the corresponding transformation matrices. Unlike most structured sparse models, our suggested method does not require the nonlocal self-similarity assumption or patch clustering algorithms to find similar grouped patches either in the image under test or in an external dataset. Finally, an effective optimization algorithm is designed to solve the corresponding sparse inverse problem. Extensive experimental comparisons with state-of-the-art image deblurring and super-resolution algorithms validate the effectiveness of our proposed method.