Robust Structured Dictionary Learning For Block Sparse Representations Using α-Divergence

Dictionary learning algorithms have been successfully used to solve a variety of signal and image processing problems. In some applications however, the observed signals may be contaminated by outliers and have a multi-subpsace structure that enables block-sparse signal representations. Based on the observation that the observed signals can be approximated as a sum of low rank matrices, a new algorithm for learning a block-structured dictionary in the presence of outliers is proposed. The proposed algorithm is obtained using a robust α-divergence based data fitting term in the algorithm cost function and derived via sequential penalized low rank matrix approximation. Experimental results illustrating the performance of the proposed algorithm compared to some state-of-the-art algorithms are provided.