Distributed Approximate Message Passing for Compressed Sensing

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...

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...

Performance Analysis of Approximate Message Passing for Distributed Compressed Sensing

Bayesian approximate message passing (BAMP) is an efficient method in compressed sensing that is nearly optimal in the minimum mean squared error (MMSE) sense. Bayesian approximate message passing (BAMP) performs joint recovery of multiple vectors with identical support and accounts for correlations in the signal of interest and in the noise. In this paper, we show how to reduce the complexity ...

Approximate message-passing with spatially coupled structured operators, with applications to compressed sensing and sparse superposition codes

We study a compressed sensing solver called Approximate Message-Passing when the i.i.d matrices —for which it has been designed— are replaced by structured operators allowing computationally fast matrix multiplications. We show empirically that after proper randomization, the underlying structure of the operators does not significantly affect the performances of the solver. In particular, for s...

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