A sparse Kaczmarz solver and a linearized Bregman method for online compressed sensing

Author

Lorenz, Dirk A. ; Wenger, Stephan ; Schopfer, Frank ; Magnor, Marcus

Author_Institution

Inst. for Anal. & Algebra, Tech. Univ. Braunschweig, Braunschweig, Germany

fYear

2014

fDate

27-30 Oct. 2014

Firstpage

1347

Lastpage

1351

Abstract

An algorithmic framework to compute sparse or minimal-TV solutions of linear systems is proposed. The framework includes both the Kaczmarz method and the linearized Bregman method as special cases and also several new methods such as a sparse Kaczmarz solver. The algorithmic framework has a variety of applications and is especially useful for problems in which the linear measurements are slow and expensive to obtain. We present examples for online compressed sensing, TV tomographic reconstruction and radio interferometry.

Keywords

compressed sensing; linear systems; TV tomographic reconstruction; linear measurements; linear systems; linearized Bregman method; minimal-TV solutions; online compressed sensing; radio interferometry; sparse Kaczmarz solver; Compressed sensing; Convergence; Image reconstruction; Imaging; Linear systems; Signal processing algorithms; Sparse matrices; Kaczmarz method; Sparse solutions; compressed sensing; linearized Bregman method; radio inter-ferometry;

fLanguage

English

Publisher

ieee

Conference_Titel

Image Processing (ICIP), 2014 IEEE International Conference on

Conference_Location

Paris

Type

conf

DOI

10.1109/ICIP.2014.7025269

Filename

7025269