Dictionary Design for Sparse Signal Representations Using K-SVD with Sparse Bayesian Learning

Sparse representations of signals in overcomplete basis have attracted much interest during the past two decades. One problem in the area of sparse signal representations is to find an ideal overcomplete basis (dictionary) to represent a given set of training signals appropriately. The K-SVD algorithm has achieved this feat with much success but suffers from the problem of underutilization of certain signal-atoms in the basis. This paper proposes to counter this problem by using Sparse Bayesian Learning in the initial stage of the K-SVD algorithm. Sparse Bayesian Learning offers gradual convergence of the learning algorithm from a non-sparse representation of the signals to a sparse representation as the iterations progress, giving the training vectors a good enough chance to "spread out" over the dictionary. The proposed algorithm is compared to the conventional K-SVD algorithm with promising results.