Message-passing algorithms for compressed sensing

DL Donoho, A Maleki… - Proceedings of the …, 2009 - National Acad Sciences
Compressed sensing aims to undersample certain high-dimensional signals yet accurately
reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible …

Probabilistic reconstruction in compressed sensing: algorithms, phase diagrams, and threshold achieving matrices

F Krzakala, M Mézard, F Sausset, Y Sun… - Journal of Statistical …, 2012 - iopscience.iop.org
Compressed sensing is a signal processing method that acquires data directly in a
compressed form. This allows one to make fewer measurements than were considered …

LDPC codes for compressed sensing

AG Dimakis, R Smarandache… - IEEE Transactions on …, 2012 - ieeexplore.ieee.org
We present a mathematical connection between channel coding and compressed sensing.
In particular, we link, on the one hand, channel coding linear programming decoding (CC …

Approximate message passing algorithms for compressed sensing

A Maleki - 2010 - search.proquest.com
Compressed sensing refers to a growing body of techniques that'undersample'high-
dimensional signals and yet recover them accurately. Such techniques make fewer …

Sparse recovery of nonnegative signals with minimal expansion

MA Khajehnejad, AG Dimakis, W Xu… - IEEE Transactions on …, 2010 - ieeexplore.ieee.org
We investigate the problem of reconstructing a high-dimensional nonnegative sparse vector
from lower-dimensional linear measurements. While much work has focused on dense …

The effect of spatial coupling on compressive sensing

S Kudekar, HD Pfister - 2010 48th Annual Allerton Conference …, 2010 - ieeexplore.ieee.org
Recently, it was observed that spatially-coupled LDPC code ensembles approach the
Shannon capacity for a class of binary-input memoryless symmetric (BMS) channels. The …

Computing linear transformations with unreliable components

Y Yang, P Grover, S Kar - IEEE Transactions on Information …, 2017 - ieeexplore.ieee.org
We consider the problem of computing a binary linear transformation when all circuit
components are unreliable. Two models of unreliable components are considered …

Verification decoding of high-rate LDPC codes with applications in compressed sensing

F Zhang, HD Pfister - IEEE Transactions on Information Theory, 2012 - ieeexplore.ieee.org
This paper considers the performance of (j, k)-regular low-density parity-check (LDPC)
codes with message-passing (MP) decoding algorithms in the high-rate regime. In particular …

Sub-linear time support recovery for compressed sensing using sparse-graph codes

X Li, D Yin, S Pawar, R Pedarsani… - IEEE Transactions on …, 2019 - ieeexplore.ieee.org
We study the support recovery problem for compressed sensing, where the goal is to
reconstruct the sparsity pattern of a high-dimensional K-sparse signal x∈ ℝ N, as well as the …

LP decoding meets LP decoding: a connection between channel coding and compressed sensing

AG Dimakis, PO Vontobel - 2009 47th Annual Allerton …, 2009 - ieeexplore.ieee.org
This is a tale of two linear programming decoders, namely channel coding linear
programming decoding (CC-LPD) and compressed sensing linear programming decoding …