From Event: SPIE Commercial + Scientific Sensing and Imaging, 2018
The problem of sparse support recovery in Multiple Measurement Vector (MMV) models is considered, where the support size (K) can be larger than the dimension (M) of each measurement vector. Most results in literature address the case where K < M. We propose a sequential detector for the MMV problem, which despite its simplicity, it can recover supports of size K = O(M2), for suitable measurement matrices, with a probability of error decaying to zero exponentially fast as the number of independent measurement vectors (L) goes to infinity. By exactly characterizing the distribution of the detection statistic, we derive explicit forms for the error exponent. We show that the required conditions on the measurement matrix can be met for equiangular tight frames. Although certain constructive methods show existence of equiangular tight frames of size N > M (N being the number of columns), the question of existence of equiangular tight frames of size N = O(M2), for arbitrarily large M, is still an open problem. We review some of the well-known results on this topic, and make connections to the support recovery problem when K > M.
Ali Koochakzadeh and Piya Pal, "A greedy approach for correlation-aware sparse support recovery," Proc. SPIE 10658, Compressive Sensing VII: From Diverse Modalities to Big Data Analytics, 106580C (Presented at SPIE Commercial + Scientific Sensing and Imaging: April 18, 2018; Published: 14 May 2018); https://doi.org/10.1117/12.2310199.
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