Message Passing Algorithms for Compressed Sensing

A Matching Pursuit Generalized Approximate Message Passing Algorithm

This paper proposes a novel matching pursuit generalized approximate message passing (MPGAMP) algorithm which explores the support of sparse representation coefficients step by step, and estimates the mean and variance of non-zero elements at each step based on a generalized-approximate-message-passing-like scheme. In contrast to the classic message passing based algorithms and matching pursuit...

Graphical Models Concepts in Compressed Sensing

This paper surveys recent work in applying ideas from graphical models and message passing algorithms to solve large scale regularized regression problems. In particular, the focus is on compressed sensing reconstruction via l1 penalized least-squares (known as LASSO or BPDN). We discuss how to derive fast approximate message passing algorithms to solve this problem. Surprisingly, the analysis ...

How to Design Message Passing Algorithms for Compressed Sensing

Finding fast first order methods for recovering signals from compressed measurements is a problem of interest in applications ranging from biology to imaging. Recently, the authors proposed a class of low-complexity algorithms called approximate message passing or AMP. The new algorithms were shown, through extensive simulations and mathematical analysis, to exhibit very fast convergence rate a...

State Evolution for General Approximate Message Passing Algorithms, with Applications to Spatial Coupling

We consider a class of approximated message passing (AMP) algorithms and characterize their high-dimensional behavior in terms of a suitable state evolution recursion. Our proof applies to Gaussian matrices with independent but not necessarily identically distributed entries. It covers – in particular– the analysis of generalized AMP, introduced by Rangan, and of AMP reconstruction in compresse...

Approximate Message Passing Algorithms for Compressed Sensing a Dissertation Submitted to the Department of Electrical Engineering and the Committee on Graduate Studies of Stanford University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

Denoising Message Passing for X-ray Computed Tomography Reconstruction

X-ray Computed Tomography (CT) reconstruction from sparse number of views is becoming a powerful way to reduce either the radiation dose or the acquisition time in CT systems but still requires a huge computational time. This paper introduces an approximate Bayesian inference framework for CT reconstruction based on a family of denoising approximate message passing (DCT-AMP) algorithms able to ...