{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,5,10]],"date-time":"2024-05-10T02:31:47Z","timestamp":1715308307039},"reference-count":8,"publisher":"Wiley","issue":"2-3","license":[{"start":{"date-parts":[[2006,2,15]],"date-time":"2006-02-15T00:00:00Z","timestamp":1139961600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[2006,3]]},"abstract":"Abstract<\/jats:title>This paper deals with the solution of a non\u2010linear ill\u2010conditioned inverse problem arising in digital image registration. In the first part of the paper, we define the problem as the minimization of a regularized non\u2010linear least\u2010squares functional, which measures the image difference and smoothness of the transformation. We study inexact Newton methods for solving this problem, i.e. we linearize the functional around a current approximation and replace the Hessian by a suitable operator in order to obtain well\u2010posed subproblems in each step of the iteration.<\/jats:p>These anisotropic subproblems are solved using a multigrid solver. Due to the anisotropy in the coefficients of the underlying equations, standard multigrid solvers suffer from poor convergence rates. We discuss modifications to the multigrid components, specifically to the smoothing procedure, the interpolation and the coarse grid correction. Numerical results that demonstrate the improvements obtained with these new components are given. Copyright \u00a9 2006 John Wiley & Sons, Ltd.<\/jats:p>","DOI":"10.1002\/nla.477","type":"journal-article","created":{"date-parts":[[2006,2,15]],"date-time":"2006-02-15T10:50:20Z","timestamp":1140000620000},"page":"215-229","source":"Crossref","is-referenced-by-count":44,"title":["A multigrid method for anisotropic PDEs in elastic image registration"],"prefix":"10.1002","volume":"13","author":[{"given":"Lars","family":"H\u00f6mke","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,2,15]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1007958904918"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-322-94877-9"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1023\/B:BITN.0000009940.58397.98"},{"key":"e_1_2_1_5_2","volume-title":"Multigrid","author":"Trottenberg U","year":"2001"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(82)90057-2"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1137\/0902035"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(90)90252-U"},{"key":"e_1_2_1_9_2","volume-title":"Technical Report","author":"Kalmoun EM","year":"2003"}],"container-title":["Numerical Linear Algebra with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnla.477","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/nla.477","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,30]],"date-time":"2023-08-30T10:06:27Z","timestamp":1693389987000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/nla.477"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,2,15]]},"references-count":8,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[2006,3]]}},"alternative-id":["10.1002\/nla.477"],"URL":"https:\/\/doi.org\/10.1002\/nla.477","archive":["Portico"],"relation":{},"ISSN":["1070-5325","1099-1506"],"issn-type":[{"value":"1070-5325","type":"print"},{"value":"1099-1506","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,2,15]]}}}