Monday, January 05, 2015

Recovery from Linear Measurements with Complexity-Matching Universal Signal Estimation - implementation -

Dror just sent me the following:

Hello Igor,  
Here's a link with an improved implementation of our universal compressed sensing algorithm: 
In recent work
Junan, Marco, and I significantly improved our universal algorithm from 2011, often by 5 dB or more. The new algorithm is often competitive in terms of reconstruction quality with other Bayesian approaches *although* our algorithm does not know the input distribution.

Dror Baron, Ph.D.
Assistant Professor
Electrical and Computer Engineering Department
North Carolina State University
Thanks Dror !

Recovery from Linear Measurements with Complexity-Matching Universal Signal Estimation by Junan Zhu, Dror Baron, Marco F. Duarte
We study the compressed sensing (CS) signal estimation problem where an input signal is measured via a linear matrix multiplication under additive noise. While this setup usually assumes sparsity or compressibility in the input signal during recovery, the signal structure that can be leveraged is often not known a priori. In this paper, we consider universal CS recovery, where the statistics of a stationary ergodic signal source are estimated simultaneously with the signal itself. Inspired by Kolmogorov complexity and minimum description length, we focus on a maximum a posteriori (MAP) estimation framework that leverages universal priors to match the complexity of the source. Our framework can also be applied to general linear inverse problems where more measurements than in CS might be needed. We provide theoretical results that support the algorithmic feasibility of universal MAP estimation using a Markov chain Monte Carlo implementation, which is computationally challenging. We incorporate some techniques to accelerate the algorithm while providing comparable and in many cases better reconstruction quality than existing algorithms. Experimental results show the promise of universality in CS, particularly for low-complexity sources that do not exhibit standard sparsity or compressibility.
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