AMP-MMV: Approximate Message Passing Multiple Measurement Vector

Justin Ziniel just sent me the following:

....I know from reading your blog that you always appreciate it when people provide code to the CS community to accompany their manuscripts. With that in mind, I wanted to share with you a link to a website that I and my adviser, Phil Schniter, put together for an algorithm that we recently proposed for the multiple measurement vector (MMV) problem, which we call AMP-MMV. The website can be reached from http://www.ece.osu.edu/~schniter/turboAMPmmv, and has all of our code available for download, links to our recent Asilomar and arXiv manuscripts, as well as a tutorial on how to use our code. We would be very grateful if you could share this information with your readers!

Our approach is based on recently developed approximate message passing (AMP) techniques, and is designed to work in cases where there is significant column correlation in the row-sparse signal matrix, X. Our experiments suggest that AMP-MMV offers an outstanding performance-complexity tradeoff. In addition, it has the ability to learn our probabilistic signal model parameters automatically from the data, reducing the number of knobs to tune. We'd welcome any feedback you or your readers might have.

Thanks Justin ! From the first page of the AMP-MMV site:

AMP-MMV is a recently developed Bayesian algorithm for solving the multiple measurement vector (MMV) problem in compressed sensing, in cases with (possibly) substantial amplitude correlation across time. The technique leverages recent advances in approximate message passing (AMP) in order to rapidly obtain accurate solutions in high-dimensional settings.

The tutorial is here. The attendant paper featuring this algorithm are:Efficient Message Passing-Based Inference in the Multiple Measurement Vector Problem by Justin Ziniel and Philip Schniter  The abstract reads:

In this work, a Bayesian approximate message passing algorithm is proposed for solving the multiple measurement vector (MMV) problem in compressive sensing, in which a collection of sparse signal vectors that share a common support are recovered from undersampled noisy measurements. The algorithm, AMP-MMV, is capable of exploiting temporal correlations in the amplitudes of non-zero coefficients, and provides soft estimates of the signal vectors as well as the underlying support. Central to the proposed approach is an extension of recently developed approximate message passing (AMP) techniques to the amplitude-correlated MMV setting. Aided by these techniques, AMP-MMV offers a computational complexity that is linear in all problem dimensions. In order to allow for automatic parameter tuning, an expectation-maximization algorithm that complements AMP-MMV is described. Finally, a numerical study demonstrates the power of the proposed approach and its particular suitability for application to high-dimensional problems.

Efficient High-Dimensional Inference in the Multiple Measurement Vector Problem by Justin Ziniel and Philip Schniter  The abstract reads:

In this work, a Bayesian approximate message passing algorithm is proposed for solving the multiple measurement vector (MMV) problem in compressive sensing, in which a collection of sparse signal vectors that share a common support are recovered from undersampled noisy measurements. The algorithm, AMP-MMV, is capable of exploiting temporal correlations in the amplitudes of non-zero coefficients, and provides soft estimates of the signal vectors as well as the underlying support. Central to the proposed approach is an extension of recently developed approximate message passing techniques to the amplitude-correlated MMV setting. Aided by these techniques, AMP-MMV offers a computational complexity that is linear in all problem dimensions. In order to allow for automatic parameter tuning, an expectation-maximization algorithm that complements AMP-MMV is described. Finally, a detailed numerical study demonstrates the power of the proposed approach and its particular suitability for application to high-dimensional problems.

Obviously, the AMP-MMV solver is now part of the Matrix Factorization Jungle page.

Liked this entry ? subscribe to Nuit Blanche's feed, there's more where that came from. You can also subscribe to Nuit Blanche by Email, explore the Big Picture in Compressive Sensing or the Matrix Factorization Jungle and join the conversations on compressive sensing, advanced matrix factorization and calibration issues on Linkedin.