A Robust Parallel Algorithm for Combinatorial Compressed Sensing - 2018


It was shown in previous work that a vector x E R n with at most k <; n nonzeros will be recovered from an expander sketch Ax in O(nnz(A) log k) operations via the parallel-I 0 decoding algorithm, where nnz(A) denotes the quantity of nonzero entries in an exceedingly E R m×n . In this Project, we present the strong-I zero decoding algorithm, that robustifies parallel-b zero when the sketch Ax is corrupted by additive noise. This robustness is achieved by approximating the asymptotic posterior distribution of values in the sketch given its corrupted measurements. We tend to offer analytic expressions that approximate these posteriors under the assumptions that the nonzero entries within the signal and also the noise are drawn from continuous distributions. Numerical experiments presented show that robust-I 0 is superior to existing greedy and combinatorial compressed sensing algorithms in the presence of little to moderate signal-to-noise ratios within the setting of Gaussian signals and Gaussian additive noise.

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