Bregman iterative algorithms for ℓ1-minimization with applications to compressed sensing

Bregman iterative algorithms for ℓ1-minimization with applications to compressed sensing (2008)

by Wotao Yin , Stanley Osher , Donald Goldfarb , Jerome Darbon

Venue:	SIAM J. Imaging Sci
Citations:	35 - 7 self

Datum	Value	Source
TITLE	Bregman iterative algorithms for ℓ1-minimization with applications to compressed sensing	INFERENCE
AUTHOR NAME	Wotao Yin	SVM HeaderParse 0.2
AUTHOR NAME	Stanley Osher	SVM HeaderParse 0.2
AUTHOR NAME	Donald Goldfarb	SVM HeaderParse 0.2
AUTHOR NAME	Jerome Darbon	SVM HeaderParse 0.2
ABSTRACT	Abstract. We propose simple and extremely efficient methods for solving the basis pursuit problem min{‖u‖1: Au = f,u ∈ R n}, which is used in compressed sensing. Our methods are based on Bregman iterative regularization, and they give a very accurate solution after solving only a very small number of 1 instances of the unconstrained problem minu∈Rn μ‖u‖1 + 2 ‖Au−fk ‖ 2 2 for given matrix A and vector f k. We show analytically that this iterative approach yields exact solutions in a finite number of steps and present numerical results that demonstrate that as few as two to six iterations are sufficient in most cases. Our approach is especially useful for many compressed sensing applications where matrix-vector operations involving A and A ⊤ can be computed by fast transforms. Utilizing a fast fixed-point continuation solver that is based solely on such operations for solving the above unconstrained subproblem, we were able to quickly solve huge instances of compressed sensing problems on a standard PC.	SVM HeaderParse 0.2
YEAR	2008	INFERENCE
VENUE	SIAM J. Imaging Sci	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	143--168	INFERENCE
CITATIONS	100 found	ParsCit 1.0