K-SVD with reference: an initialization method for dictionary learning

Recently, sparse signal recovery has received a lot attention for its wide real applications. Such a problem can be solved better if using a proper dictionary. Therefore, dictionary learning has become a promising direction and still been an open topic. As one of the greatest potential candidates, K-singular value decomposition (K-SVD) algorithm has been recognized by users. However, its performance has reached limitations of further improvement since it cannot consider the dependence between atoms. In this paper, we mine the inner structure of signals using their autocorrelations and make these prior as the reference. Based on these references, we present a new technique, which incorporates these references to K-SVD algorithm and provide a new method to initialize the dictionary. Experiments on synthetic data and image data show that the proposed algorithm has higher convergence ratio and lower error than the original K-SVD algorithm. Also, it performs better and more stable for sparse signal recovery.