Reduce and Boost: Recovering Arbitrary Sets of Jointly Sparse Vectors

The rapid developing area of compressed sensing suggests that a sparse vector lying in a high dimensional space can be accurately and efficiently recovered from only a small set of non-adaptive linear measurements, under appropriate conditions on the measurement matrix. The vector model has been extended both theoretically and practically to a finite set of sparse vectors sharing a common sparsity pattern. In this paper, we treat a broader framework in which the goal is to recover a possibly infinite set of jointly sparse vectors. Extending existing algorithms to this model is difficult due to the infinite structure of the sparse vector set. Instead, we prove that the entire infinite set of sparse vectors can be recovered by solving a single, reduced-size finite-dimensional problem, corresponding to recovery of a finite set of sparse vectors. We then show that the problem can be further reduced to the basic model of a single sparse vector by randomly combining the measurements. Our app...

• Type: Journal
• Year: 2008
• Where: TSP
• Authors: Moshe Mishali, Yonina C. Eldar
• Keywords: Finite Set, Single Sparse Vector, Sparse Vector, TSP 2008