Rician denoising and deblurring using sparse representation prior and nonconvex total variation

We propose a sparse representation based model to restore an image corrupted by blurring and Rician noise. Our model is composed of a nonconvex data-fidelity term and two regularization terms involving a sparse representation prior and a nonconvex total variation. The sparse representation prior, using image patches, provides restored images with well-preserved repeated patterns and small details, whereas the non-convex total variation enables the preservation of edges. Moreover, the regularization terms are mutually complementary in removing artifacts. To realize our nonconvex model, we adopt the penalty method and the alternating minimization method. The K-SVD algorithm is utilized for learning dictionaries. Numerical experiments demonstrate that the proposed model is superior to state-of-the-art models, in terms of visual quality and certain image quality measurements.