• Optimal Phase Transitions in C...

Treffer: Optimal Phase Transitions in Compressed Sensing

Title:
Optimal Phase Transitions in Compressed Sensing
Authors:
YIHONG WU, VERDU, Sergio
Source:
IEEE transactions on information theory. 58(10):6241-6263
Publisher Information:
New York, NY: Institute of Electrical and Electronics Engineers, 2012.
Publication Year:
2012
Physical Description:
print, 76 ref
Original Material:
INIST-CNRS
Subject Terms:
Telecommunications, Télécommunications, Sciences exactes et technologie, Exact sciences and technology, Sciences appliquees, Applied sciences, Telecommunications et theorie de l'information, Telecommunications and information theory, Théorie de l'information, du signal et des communications, Information, signal and communications theory, Théorie de l'information, Information theory, Théorie du signal et des communications, Signal and communications theory, Codage, codes, Coding, codes, Echantillonnage, quantification, Sampling, quantization, Algorithme, Algorithm, Algoritmo, Circuit codeur, Coding circuit, Circuito codificación, Codage linéaire, Linear coding, Codificación lineal, Codage source canal, Joint source channel coding, Codificación fuente canal, Décodage, Decoding, Desciframiento, Erreur quadratique moyenne, Mean square error, Error medio cuadrático, Etude statistique, Statistical study, Estudio estadístico, Matrice aléatoire, Random matrix, Matriz aleatoria, Modélisation, Modeling, Modelización, Méthode heuristique, Heuristic method, Método heurístico, Méthode statistique, Statistical method, Método estadístico, Probabilité erreur, Error probability, Probabilidad error, Signal analogique, Analog signal, Señal analógica, Signal entrée, Input signal, Señal entrada, Théorie Renyi, Renyi theory, Teoría Renyi, Théorie Shannon, Shannon theory, Teoría Shannon, Transition phase, Phase transitions, Transición fase, Echantillonnage parcimonieux, Compressed sensing, Rényi information dimension, joint source-channel coding, minimum mean-square error (MMSE) dimension, phase transition, random matrix
Document Type:
Fachzeitschrift Article
File Description:
text
Language:
English
Author Affiliations:
Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, PA 19104, United States
Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, United States
ISSN:
0018-9448
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=26403661
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Telecommunications and information theory
Accession Number:
edscal.26403661
Database:
PASCAL Archive

Weitere Informationen

Compressed sensing deals with efficient recovery of analog signals from linear encodings. This paper presents a statistical study of compressed sensing by modeling the input signal as an i.i.d. process with known distribution. Three classes of encoders are considered, namely optimal nonlinear, optimal linear, and random linear encoders. Focusing on optimal decoders, we investigate the fundamental tradeoff between measurement rate and reconstruction fidelity gauged by error probability and noise sensitivity in the absence and presence of measurement noise, respectively. The optimal phase-transition threshold is determined as a functional of the input distribution and compared to suboptimal thresholds achieved by popular reconstruction algorithms. In particular, we show that Gaussian sensing matrices incur no penalty on the phase-transition threshold with respect to optimal nonlinear encoding. Our results also provide a rigorous justification of previous results based on replica heuristics in the weak-noise regime.