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Quadratically fast IRLS for sparse signal recovery

Chiara Ravazzi, Enrico Magli

2015 Signal Processing with Adaptive Sparse Structured Representations (SPARS 2015), July 6-9, 2015, Cambridge, UK.


We present a new class of iterative algorithms for sparse recovery problems that combine iterative support detection and estimation.
More precisely, these methods use a two state Gaussian scale mixture as a proxy for the signal model and can be interpreted both as iteratively reweighted least squares (IRLS) and Expectation/Maximization (EM) algorithms for the constrained maximization of the log-likelihood function. Under certain conditions, these methods are proved to converge to a sparse solution and to be quadratically fast in a neighborhood of that sparse solution, outperforming classical IRLS for ℓτ-minimization. Numerical experiments validate the theoretical derivations and show that these new reconstruction schemes outperform classical IRLS for  ℓτ-minimization with τ ∈ (0, 1] in sparsity-undersampling tradeoff.

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