## A limited-memory, quasi-Newton preconditioner for nonnegatively constrained image reconstruction

JOSA A, Vol. 21, Issue 5, pp. 724-731 (2004)

http://dx.doi.org/10.1364/JOSAA.21.000724

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### Abstract

Image reconstruction gives rise to some challenging large-scale constrained optimization problems. We consider a convex minimization problem with nonnegativity constraints that arises in astronomical imaging. To solve this problem, we use an efficient hybrid gradient projection–reduced Newton (active-set) method. By “reduced Newton,” we mean that we take Newton steps only in the inactive variables. Owing to the large size of our problem, we compute approximate reduced Newton steps by using the conjugate gradient (CG) iteration. We introduce a limited-memory, quasi-Newton preconditioner that speeds up CG convergence. A numerical comparison is presented that demonstrates the effectiveness of this preconditioner.

© 2004 Optical Society of America

**OCIS Codes**

(100.1830) Image processing : Deconvolution

(100.3010) Image processing : Image reconstruction techniques

(100.3190) Image processing : Inverse problems

**History**

Original Manuscript: September 9, 2003

Revised Manuscript: December 5, 2003

Manuscript Accepted: December 5, 2003

Published: May 1, 2004

**Citation**

Johnathan M. Bardsley, "A limited-memory, quasi-Newton preconditioner for nonnegatively constrained image reconstruction," J. Opt. Soc. Am. A **21**, 724-731 (2004)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-5-724

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