Structured sparse representation with low-rank interference

This paper proposes a novel framework that is capable of extracting the low-rank interference while simultaneously promoting sparsity-based representation of multiple correlated signals. The proposed model provides an efficient approach for the representation of multiple measurements where the underlying signals exhibit a structured sparsity representation over some proper dictionaries but the set of testing samples are corrupted by the interference from external sources. Under the assumption that the interference component forms a low-rank structure, the proposed algorithms minimize the nuclear norm of the interference to exclude it from the representation of multivariate sparse representation. An efficient algorithm based on alternating direction method of multipliers is proposed for the general framework. Extensive experimental results are conducted on two practical applications: chemical plume detection and classification in hyperspectral sequences and robust speech recognition in noisy environments to verify the effectiveness of the proposed methods.