Reconstruction of low-rank jointly sparse signals from multiple measurement vectors
The multiple measurement vectors problem approximates a set of signals sharing a common sparsity pattern simultaneously, using different linear combinations of those signals obtained through a sensing matrix. In a situation where the signal matrix has full row-rank, MUltiple SIgnal Classification (MUSIC) algorithm guarantees to recover the jointly sparse signals, but for the rank-defective case, the MUSIC performance is voided. To address such a rank deficient case, our proposed method, line search low-rank jointly sparse signals (LS-LRJSS), provides a geometric analysis of the problem by characterizing the linear dependence of the measurements with the linear coefficients that permit the reconstruction of each point from its neighbors. Moreover, a subspace analysis has been done on a Grassmann manifold to obtain the subspace that the signal matrix belongs to. Several numerical experiments evidence that the proposed method is more accurate and less time-consuming compared to existing approaches especially wherever the sparsity level of the signals increases or the number of measurement vectors decreases.
KeywordsCompressive sensing Multiple measurement vectors Joint sparsity Rank deficiency
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