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We use deterministic and probabilistic methods to analyze the performance of compressed sensing matrices constructed from Hadamard matrices and pairwise balanced designs, previously introduced by a subset of the authors.… Click to show full abstract
We use deterministic and probabilistic methods to analyze the performance of compressed sensing matrices constructed from Hadamard matrices and pairwise balanced designs, previously introduced by a subset of the authors. In this paper, we obtain upper and lower bounds on the sparsity of signals for which our matrices guarantee recovery. These bounds are tight to within a multiplicative factor of at most $4\sqrt {2}$ . We provide new theoretical results and detailed simulations, which indicate that the construction is competitive with Gaussian random matrices, and that recovery is tolerant to noise. A new recovery algorithm tailored to the construction is also given.
Journal Title: IEEE Transactions on Information Theory
Year Published: 2017
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