COHERENCE-BASED NEAR-ORACLE PERFORMANCE GUARANTEES FOR SPARSE ESTIMATION UNDER GAUSSIAN NOISE

被引：3

作者：

Ben-Haim, Zvika ^{[1
]}

Eldar, Yonina C. ^{[1
]}

Elad, Michael ^{[1
]}

机构：

[1] Technion Israel Inst Technol, IL-32000 Haifa, Israel

来源：

2010 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING | 2010年

关键词：

Sparse estimation; basis pursuit; matching pursuit; thresholding algorithm; oracle; DANTZIG SELECTOR;

D O I：

10.1109/ICASSP.2010.5495919

中图分类号：

O42 [声学];

学科分类号：

070206 ; 082403 ;

摘要：

We consider the problem of estimating a deterministic sparse vector x(0) from underdetermined measurements Ax(0) + w, where w represents white Gaussian noise and A is a given deterministic dictionary. We analyze the performance of three sparse estimation algorithms: basis pursuit denoising, orthogonal matching pursuit, and thresholding. These approaches are shown to achieve near-oracle performance with high probability, assuming that x(0) is sufficiently sparse. Our results are non-asymptotic and are based only on the coherence of A, so that they are applicable to arbitrary dictionaries.

引用

页码：3590 / 3593

页数：4

共 8 条

[1]

BENHAIM Z, IEEE T SIGNAL UNPUB

[2] SIMULTANEOUS ANALYSIS OF LASSO AND DANTZIG SELECTOR [J].

Bickel, Peter J. ;

Ritov, Ya'acov ;

Tsybakov, Alexandre B. .

ANNALS OF STATISTICS, 2009, 37 (04) :1705-1732

[3]

CANDES EJ, 2006, ACTA NUMER, P1

[4]

Candes E, 2007, ANN STAT, V35, P2313, DOI 10.1214/009053606000001523

[5] NEAR-IDEAL MODEL SELECTION BY l1 MINIMIZATION [J].

Candes, Emmanuel J. ;

Plan, Yaniv .

ANNALS OF STATISTICS, 2009, 37 (5A) :2145-2177

[6] Atomic decomposition by basis pursuit [J].

Chen, SSB ;

Donoho, DL ;

Saunders, MA .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1998, 20 (01) :33-61

[7] Stable recovery of sparse overcomplete representations in the presence of noise [J].

Donoho, DL ;

Elad, M ;

Temlyakov, VN .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2006, 52 (01) :6-18

[8]

PATI YC, 1993, P 27 AS C SIGN SYST, P40, DOI DOI 10.1109/ACSSC.1993.342465

← 1 →