Computer Science – Information Theory
Scientific paper
2012-04-25
Computer Science
Information Theory
6 pages, 1 figure. This is a corrected and updated version of the paper published in IEEE ITW'11, Paraty Brazil, October 16-20
Scientific paper
Minimum mean square error (MMSE) estimation of block sparse signals from noisy linear measurements is considered. Unlike in the standard compressive sensing setup where the non-zero entries of the signal are independently and uniformly distributed across the vector of interest, the information bearing components appear here in large mutually dependent clusters. Using the replica method from statistical physics, we derive a simple closed-form solution for the MMSE obtained by the optimum estimator. We show that the MMSE is a version of the Tse-Hanly formula with system load and MSE scaled by parameters that depend on the sparsity pattern of the source. It turns out that this is equal to the MSE obtained by a genie-aided MMSE estimator which is informed in advance about the exact locations of the non-zero blocks. The asymptotic results obtained by the non-rigorous replica method are found to have an excellent agreement with finite sized numerical simulations.
Chatterjee Saikat
Skoglund Mikael
Vehkaperä Mikko
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