Optimal recovery from compressive measurements via denoising-based approximate message passing

Christopher A. Metzler; Arian Maleki; Richard G. Baraniuk

doi:10.1109/SAMPTA.2015.7148943

Optimal recovery from compressive measurements via denoising-based approximate message passing

Christopher A. Metzler, Arian Maleki, Richard G. Baraniuk

Houston Methodist

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

7 Scopus citations

Abstract

Recently progress has been made in compressive sensing by replacing simplistic sparsity models with more powerful denoisers. In this paper, we develop a framework to predict the performance of denoising-based signal recovery algorithms based on a new deterministic state evolution formalism for approximate message passing. We compare our deterministic state evolution against its more classical Bayesian counterpart. We demonstrate that, while the two state evolutions are very similar, the deterministic framework is far more flexible. We apply the deterministic state evolution to explore the optimality of denoising-based approximate message passing (D-AMP). We prove that, while D-AMP is suboptimal for certain classes of signals, no algorithm can uniformly outperform it.

Original language	English (US)
Title of host publication	2015 International Conference on Sampling Theory and Applications, SampTA 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	508-512
Number of pages	5
ISBN (Electronic)	9781467373531
DOIs	https://doi.org/10.1109/SAMPTA.2015.7148943
State	Published - Jul 2 2015
Event	11th International Conference on Sampling Theory and Applications, SampTA 2015 - Washington, United States Duration: May 25 2015 → May 29 2015

Publication series

Name	2015 International Conference on Sampling Theory and Applications, SampTA 2015

Other

Other	11th International Conference on Sampling Theory and Applications, SampTA 2015
Country/Territory	United States
City	Washington
Period	5/25/15 → 5/29/15

Keywords

Approximate Message Passing
Compressed Sensing
Denoising
State Evolution

ASJC Scopus subject areas

Signal Processing
Statistics and Probability
Discrete Mathematics and Combinatorics

Access to Document

10.1109/SAMPTA.2015.7148943

Cite this

Metzler, C. A., Maleki, A., & Baraniuk, R. G. (2015). Optimal recovery from compressive measurements via denoising-based approximate message passing. In 2015 International Conference on Sampling Theory and Applications, SampTA 2015 (pp. 508-512). Article 7148943 (2015 International Conference on Sampling Theory and Applications, SampTA 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SAMPTA.2015.7148943

Optimal recovery from compressive measurements via denoising-based approximate message passing. / Metzler, Christopher A.; Maleki, Arian; Baraniuk, Richard G.
2015 International Conference on Sampling Theory and Applications, SampTA 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 508-512 7148943 (2015 International Conference on Sampling Theory and Applications, SampTA 2015).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Metzler, CA, Maleki, A & Baraniuk, RG 2015, Optimal recovery from compressive measurements via denoising-based approximate message passing. in 2015 International Conference on Sampling Theory and Applications, SampTA 2015., 7148943, 2015 International Conference on Sampling Theory and Applications, SampTA 2015, Institute of Electrical and Electronics Engineers Inc., pp. 508-512, 11th International Conference on Sampling Theory and Applications, SampTA 2015, Washington, United States, 5/25/15. https://doi.org/10.1109/SAMPTA.2015.7148943

Metzler CA, Maleki A, Baraniuk RG. Optimal recovery from compressive measurements via denoising-based approximate message passing. In 2015 International Conference on Sampling Theory and Applications, SampTA 2015. Institute of Electrical and Electronics Engineers Inc. 2015. p. 508-512. 7148943. (2015 International Conference on Sampling Theory and Applications, SampTA 2015). doi: 10.1109/SAMPTA.2015.7148943

Metzler, Christopher A. ; Maleki, Arian ; Baraniuk, Richard G. / Optimal recovery from compressive measurements via denoising-based approximate message passing. 2015 International Conference on Sampling Theory and Applications, SampTA 2015. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 508-512 (2015 International Conference on Sampling Theory and Applications, SampTA 2015).

@inproceedings{98d43877bb3b4384929aed416b83474d,

title = "Optimal recovery from compressive measurements via denoising-based approximate message passing",

abstract = "Recently progress has been made in compressive sensing by replacing simplistic sparsity models with more powerful denoisers. In this paper, we develop a framework to predict the performance of denoising-based signal recovery algorithms based on a new deterministic state evolution formalism for approximate message passing. We compare our deterministic state evolution against its more classical Bayesian counterpart. We demonstrate that, while the two state evolutions are very similar, the deterministic framework is far more flexible. We apply the deterministic state evolution to explore the optimality of denoising-based approximate message passing (D-AMP). We prove that, while D-AMP is suboptimal for certain classes of signals, no algorithm can uniformly outperform it.",

keywords = "Approximate Message Passing, Compressed Sensing, Denoising, State Evolution",

author = "Metzler, {Christopher A.} and Arian Maleki and Baraniuk, {Richard G.}",

note = "Publisher Copyright: {\textcopyright} 2015 IEEE.; 11th International Conference on Sampling Theory and Applications, SampTA 2015 ; Conference date: 25-05-2015 Through 29-05-2015",

year = "2015",

month = jul,

day = "2",

doi = "10.1109/SAMPTA.2015.7148943",

language = "English (US)",

series = "2015 International Conference on Sampling Theory and Applications, SampTA 2015",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "508--512",

booktitle = "2015 International Conference on Sampling Theory and Applications, SampTA 2015",

address = "United States",

}

TY - GEN

T1 - Optimal recovery from compressive measurements via denoising-based approximate message passing

AU - Metzler, Christopher A.

AU - Maleki, Arian

AU - Baraniuk, Richard G.

PY - 2015/7/2

Y1 - 2015/7/2

N2 - Recently progress has been made in compressive sensing by replacing simplistic sparsity models with more powerful denoisers. In this paper, we develop a framework to predict the performance of denoising-based signal recovery algorithms based on a new deterministic state evolution formalism for approximate message passing. We compare our deterministic state evolution against its more classical Bayesian counterpart. We demonstrate that, while the two state evolutions are very similar, the deterministic framework is far more flexible. We apply the deterministic state evolution to explore the optimality of denoising-based approximate message passing (D-AMP). We prove that, while D-AMP is suboptimal for certain classes of signals, no algorithm can uniformly outperform it.

AB - Recently progress has been made in compressive sensing by replacing simplistic sparsity models with more powerful denoisers. In this paper, we develop a framework to predict the performance of denoising-based signal recovery algorithms based on a new deterministic state evolution formalism for approximate message passing. We compare our deterministic state evolution against its more classical Bayesian counterpart. We demonstrate that, while the two state evolutions are very similar, the deterministic framework is far more flexible. We apply the deterministic state evolution to explore the optimality of denoising-based approximate message passing (D-AMP). We prove that, while D-AMP is suboptimal for certain classes of signals, no algorithm can uniformly outperform it.

KW - Approximate Message Passing

KW - Compressed Sensing

KW - Denoising

KW - State Evolution

UR - http://www.scopus.com/inward/record.url?scp=84941096284&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84941096284&partnerID=8YFLogxK

U2 - 10.1109/SAMPTA.2015.7148943

DO - 10.1109/SAMPTA.2015.7148943

M3 - Conference contribution

AN - SCOPUS:84941096284

T3 - 2015 International Conference on Sampling Theory and Applications, SampTA 2015

SP - 508

EP - 512

BT - 2015 International Conference on Sampling Theory and Applications, SampTA 2015

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 11th International Conference on Sampling Theory and Applications, SampTA 2015

Y2 - 25 May 2015 through 29 May 2015

ER -

Optimal recovery from compressive measurements via denoising-based approximate message passing

Abstract

Publication series

Other

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this