Morphological Component Image Restoration by Employing Bregmanized Sparse Regularization and Anisotropic Total Variation

Image deblurring is a fundamental problem in imaging field which often needs to recover the important structure of images. This paper addresses the image deblurring problem by considering an image as a combination of its cartoon (the piecewise smooth part of the image) and texture (the oscillation part of the image) components. To recover both of these parts, we propose the use of coupled analysis-based sparse representations to regularize the cartoon structure and the texture part of the image. We apply anisotropic total variation with a quadratic term to enhance the edges existing in the cartoon part. Furthermore, we develop a multivariable Bregman optimization method to solve the proposed image restoration model by combining the alternating minimization method and the split Bregman iteration. The experiments show that the proposed algorithm not only performs well for image decomposition, but also outperforms the previously established methods in terms of the visual residual error, the structure similarity index and the peak signal-to-noise ratio for image deblurring.