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

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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.

Original languageEnglish
Pages (from-to)724-731
Number of pages8
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Volume21
Issue number5
DOIs
StatePublished - May 2004

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