Friday, May 24, 2013

SL0-mod: Surpassing the Theoretical L_1 norm phase transition in Compressive Sennsing by Tuning the Smoother l_0 Algorithm: - implementation -

Reconstruction of an undersampled signal is at the root of compressive sensing: when is an algorithm capable of reconstructing the signal? what quality is achievable? and how much time does reconstruction require? We have considered the worst-case performance of the smoothed l_0 norm reconstruction algorithm in a noiseless setup. Through an empirical tuning of its parameters, we have improved the phase transition (capabilities) of the algorithm for fixed quality and required time. In this paper, we present simulation results thatshow a phase transition surpassing that of the theoretical `1 approach: the proposed modified algorithm obtains 1-norm phase transition with greatly reduced required computation time.
The attendant code for this modified version of SL0 is here. I wonder if this tuning coluld be further helped by making assumption on the signal to be reconstructed (beyond sparsity akak structured sparsity) ?

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