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 ℓ0 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 that show a phase transition surpassing that of the theoretical ℓ1 approach: the proposed modified algorithm obtains 1-norm phase transition with greatly reduced required computation time.
Acoustics, Speech, and Signal Processing (icassp), International Conference on, 2013, p. 6019-6023
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I E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings
2013 IEEE International Conference on Acoustics, Speech, and Signal ProcessingInternational Conference on Acoustics, Speech and Signal Processing, 2013