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
Full Article | PDF ArticleMore Like This
Yanfei Wang, Jingjie Cao, Yaxiang Yuan, Changchun Yang, and Naihua Xiu
Appl. Opt. 48(7) 1389-1401 (2009)
O. Nakamura, S. Kawata, and S. Minami
J. Opt. Soc. Am. A 5(4) 554-561 (1988)
Eric Thiébaut and Michel Tallon
J. Opt. Soc. Am. A 27(5) 1046-1059 (2010)