Domain decomposition methods for compressed sensing

Massimo Fornasier; Andreas Langer; Carola-Bibiane Schönlieb

Domain decomposition methods for compressed sensing

Massimo Fornasier, Andreas Langer, Carola-Bibiane Schönlieb

Research output: Contribution to conference › Paper

34 Downloads (Pure)

Abstract

We present several domain decomposition algorithms for sequential and parallel minimization of functionals formed by a discrepancy term with respect to data and total variation constraints. The convergence properties of the algorithms are analyzed. We provide several numerical experiments, showing the successful application of the algorithms for the restoration 1D and 2D signals in interpolation/inpainting problems respectively, and in a compressed sensing problem, for recovering piecewise constant medical-type images from partial Fourier ensembles.

Original language	English
Publication status	Published - 22 May 2009
Event	International Conference on SAMPling Theory and Applications - Marseille, France Duration: 18 May 2009 → 22 May 2009

Conference

Conference	International Conference on SAMPling Theory and Applications
Abbreviated title	SAMPTA09
Country/Territory	France
City	Marseille
Period	18/05/09 → 22/05/09

Bibliographical note

4 pages

Keywords

math.NA
65K10, 65N55, 65N21, 65Y05, 90C25, 52A41, 49M30, 49M27, 68U10

Access to Document

0902.0124v1

Cite this

@conference{1af298bb7f28408e820a77c6ce02cdfa,

title = "Domain decomposition methods for compressed sensing",

abstract = " We present several domain decomposition algorithms for sequential and parallel minimization of functionals formed by a discrepancy term with respect to data and total variation constraints. The convergence properties of the algorithms are analyzed. We provide several numerical experiments, showing the successful application of the algorithms for the restoration 1D and 2D signals in interpolation/inpainting problems respectively, and in a compressed sensing problem, for recovering piecewise constant medical-type images from partial Fourier ensembles. ",

keywords = "math.NA, 65K10, 65N55, 65N21, 65Y05, 90C25, 52A41, 49M30, 49M27, 68U10",

author = "Massimo Fornasier and Andreas Langer and Carola-Bibiane Sch{\"o}nlieb",

note = "4 pages; International Conference on SAMPling Theory and Applications, SAMPTA09 ; Conference date: 18-05-2009 Through 22-05-2009",

year = "2009",

month = may,

day = "22",

language = "English",

}

TY - CONF

T1 - Domain decomposition methods for compressed sensing

AU - Fornasier, Massimo

AU - Langer, Andreas

AU - Schönlieb, Carola-Bibiane

N1 - 4 pages

PY - 2009/5/22

Y1 - 2009/5/22

N2 - We present several domain decomposition algorithms for sequential and parallel minimization of functionals formed by a discrepancy term with respect to data and total variation constraints. The convergence properties of the algorithms are analyzed. We provide several numerical experiments, showing the successful application of the algorithms for the restoration 1D and 2D signals in interpolation/inpainting problems respectively, and in a compressed sensing problem, for recovering piecewise constant medical-type images from partial Fourier ensembles.

AB - We present several domain decomposition algorithms for sequential and parallel minimization of functionals formed by a discrepancy term with respect to data and total variation constraints. The convergence properties of the algorithms are analyzed. We provide several numerical experiments, showing the successful application of the algorithms for the restoration 1D and 2D signals in interpolation/inpainting problems respectively, and in a compressed sensing problem, for recovering piecewise constant medical-type images from partial Fourier ensembles.

KW - math.NA

KW - 65K10, 65N55, 65N21, 65Y05, 90C25, 52A41, 49M30, 49M27, 68U10

M3 - Paper

T2 - International Conference on SAMPling Theory and Applications

Y2 - 18 May 2009 through 22 May 2009

ER -

Domain decomposition methods for compressed sensing

Abstract

Conference

Bibliographical note

Keywords

Access to Document

Fingerprint

Cite this