Imaging Inverse Problem Using Sparse Representation with Adaptive Dictionary Learning

Abstract

Sparse representation is one of the powerful emerging statistical techniques for modeling images. This representation approximates the image as a combination of the codewords within a dictionary which is over complete. Recent years have seen a tremendous growth in the field of sparse representation. Here a method is proposed for image inversing by using iterative deblurring based on sparse representation of an image which is uniformly blurred. The key idea behind this methodology is the sparseness of natural images in some domain. The quality of recovered image majorly depends on the domain or the dictionaries that are used to represent it. In this paper, the K-SVD algorithm is used to train thegroup of codewords from a set of quality natural image patches. For each of the local patch within the blurred image, the best suited sub-dictionary from the trained dictionary data base is selected. In addition, a smoothness regularization constraint is added that prevents the reblurring of the image edges. For numerical stability the sparsity weight is adaptively computed which also improves the reconstructed image quality. Comparative study on some of the existing restoration algorithm proves the proposed method outperforms them all.