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A complete analysis of the proposed model reduction approach is given in a functional analytic setting and the efficient numerical construction of the reduced order models as well as of their application for the numerical solution of the inverse problem is discussed. In summary, the setup of a low-rank approximation can be achieved in an offline stage at essentially the same cost as a single evaluation of the forward operator, while the actual solution of the inverse problem in the online phase can be done with extremely high efficiency. The theoretical results are illustrated by application to a typical model problem in fluorescence optical tomography.<\/jats:p>","DOI":"10.1007\/s00211-021-01224-5","type":"journal-article","created":{"date-parts":[[2021,8,16]],"date-time":"2021-08-16T10:02:57Z","timestamp":1629108177000},"page":"889-917","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A model reduction approach for inverse problems with operator valued data"],"prefix":"10.1007","volume":"148","author":[{"given":"J\u00fcrgen","family":"D\u00f6lz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Herbert","family":"Egger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matthias","family":"Schlottbom","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,8,16]]},"reference":[{"key":"1224_CR1","doi-asserted-by":"publisher","first-page":"123010","DOI":"10.1088\/0266-5611\/25\/12\/123010","volume":"25","author":"SR Arridge","year":"2009","unstructured":"Arridge, S.R., Schotland, J.C.: Optical tomography: forward and inverse problems. 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