Show simple item record

dc.contributorVirginia Tech
dc.contributor.authorde Sturler, E.
dc.contributor.authorKilmer, M. E.
dc.date.accessioned2014-05-28T18:35:09Z
dc.date.available2014-05-28T18:35:09Z
dc.date.issued2011
dc.identifier.citationde Sturler, E.; Kilmer, M. E., "A regularized Gauss-Newton trust region approach to imaging in diffuse optical tomography," SIAM J. Sci. Comput., 33(5), 3057-3086, (2011). DOI: 10.1137/100798181
dc.identifier.issn1064-8275
dc.identifier.urihttp://hdl.handle.net/10919/48157
dc.description.abstractWe present a new algorithm for the solution of nonlinear least squares problems arising from parameterized imaging problems with diffuse optical tomographic data [D. Boas et al., IEEE Signal Process. Mag., 18 (2001), pp. 57-75]. The parameterization arises from the use of parametric level sets for regularization [M.E. Kilmer et al., Proc. SPIE, 5559 (2004), pp. 381-391], [A. Aghasi, M.E. Kilmer, and E.L. Miller, SIAM J. Imaging Sci., 4 (2011), pp. 618-650]. Such problems lead to Jacobians that have relatively few columns, a relatively modest number of rows, and are ill-conditioned. Moreover, such problems have function and Jacobian evaluations that are computationally expensive. Our optimization algorithm is appropriate for any inverse or imaging problem with those characteristics. In fact, we expect our algorithm to be effective for more general problems with ill-conditioned Jacobians. The algorithm aims to minimize the total number of function and Jacobian evaluations by analyzing which spectral components of the Gauss-Newton direction should be discarded or damped. The analysis considers for each component the reduction of the objective function and the contribution to the search direction, restricting the computed search direction to be within a trust region. The result is a truncated SVD-like approach to choosing the search direction. However, we do not necessarily discard components in order of decreasing singular value, and some components may be scaled to maintain fidelity to the trust region model. Our algorithm uses the Basic Trust Region Algorithm from [A.R. Conn, N.I.M. Gould, and Ph. L. Toint, Trust-Region Methods, SIAM, Philadelphia, 2000]. We prove that our algorithm is globally convergent to a critical point. Our numerical results show that the new algorithm generally outperforms competing methods applied to the DOT imaging problem with parametric level sets, and regularly does so by a significant factor.
dc.description.sponsorshipNSF DMR-0325939, 0139968, 0342559
dc.language.isoen_US
dc.publisherSiam Publications
dc.subjectnonlinear least squares
dc.subjectgauss-newton
dc.subjectlevenberg-marquardt
dc.subjectoptimization
dc.subjectregularization
dc.subjectdiffuse optical tomography
dc.subjectill-posed problems
dc.subjectlevel set methods
dc.subjectparameter estimation problems
dc.subjectlinear least-squares
dc.subjectinverse problems
dc.subjectmathematics, applied
dc.titleA regularized Gauss-Newton trust region approach to imaging in diffuse optical tomography
dc.typeArticle - Refereed
dc.identifier.urlhttp://epubs.siam.org/doi/abs/10.1137/100798181
dc.date.accessed2014-05-27
dc.title.serialSiam Journal on Scientific Computing
dc.identifier.doihttps://doi.org/10.1137/100798181


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record