Rich just sent me the following:
hi igor -we have been working on integrating advanced denoising algorithms into compressive sensing recovery algorithms and have found that approximate message passing (AMP) provides a flexible platform that can support a variety of denoisers since the Onsager correction Gaussianizes the error at each iteration. for image recovery, coupling AMP with the BM3D denoiser and the correct Onsager correction offers state-of-the-art performance. our preprint has a range of comparisons with other approaches and also an in depth analysis of the approach. i thought it might be interesting to your audience. thanks!richb
Richard G. Baraniuk
Victor E. Cameron Professor of Electrical and Computer Engineering
Founder and Director, Connexions and OpenStax College
A denoising algorithm seeks to remove perturbations or errors from a signal. The last three decades have seen extensive research devoted to this arena, and as a result, today's denoisers are highly optimized algorithms that effectively remove large amounts of additive white Gaussian noise. A compressive sensing (CS) reconstruction algorithm seeks to recover a structured signal acquired using a small number of randomized measurements. Typical CS reconstruction algorithms can be cast as iteratively estimating a signal from a perturbed observation. This paper answers a natural question: How can one effectively employ a generic denoiser in a CS reconstruction algorithm? In response, in this paper, we develop a denoising-based approximate message passing (D-AMP) algorithm that is capable of high-performance reconstruction. We demonstrate that, for an appropriate choice of denoiser, D-AMP offers state-of-the-art CS recovery performance for natural images. We explain the exceptional performance of D-AMP by analyzing some of its theoretical features. A critical insight in our approach is the use of an appropriate Onsager correction term in the D-AMP iterations, which coerces the signal perturbation at each iteration to be very close to the white Gaussian noise that denoisers are typically designed to remove.
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