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 Article
OSA Recommended Articles
Regularizing active set method for nonnegatively constrained ill-posed multichannel image restoration problem

Yanfei Wang, Jingjie Cao, Yaxiang Yuan, Changchun Yang, and Naihua Xiu
Appl. Opt. 48(7) 1389-1401 (2009)

Fast maximum-likelihood image-restoration algorithms for three- dimensional fluorescence microscopy

Joanne Markham and José-Angel Conchello
J. Opt. Soc. Am. A 18(5) 1062-1071 (2001)

Finite element-wavelet hybrid algorithm for atmospheric tomography

Mykhaylo Yudytskiy, Tapio Helin, and Ronny Ramlau
J. Opt. Soc. Am. A 31(3) 550-560 (2014)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (5)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (52)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription