{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:37:36Z","timestamp":1776847056955,"version":"3.51.2"},"reference-count":33,"publisher":"American Mathematical Society (AMS)","issue":"281","license":[{"start":{"date-parts":[[2013,6,7]],"date-time":"2013-06-07T00:00:00Z","timestamp":1370563200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    In this paper we introduce a novel adaptive approach for solving\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script l Superscript 1\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>\n                              \u2113\n                              \n                            <\/mml:mi>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">\\ell ^1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -minimization problems as frequently arising in compressed sensing, which is based on the recently introduced inverse scale space method. The scheme allows to efficiently compute minimizers by solving a sequence of low-dimensional nonnegative least-squares problems.\n                  <\/p>\n                  <p>We provide a detailed convergence analysis in a general setup as well as refined results under special conditions. In addition, we discuss experimental observations in several numerical examples.<\/p>","DOI":"10.1090\/s0025-5718-2012-02599-3","type":"journal-article","created":{"date-parts":[[2012,6,7]],"date-time":"2012-06-07T08:31:56Z","timestamp":1339057916000},"page":"269-299","source":"Crossref","is-referenced-by-count":34,"title":["An adaptive inverse scale space method for compressed sensing"],"prefix":"10.1090","volume":"82","author":[{"given":"Martin","family":"Burger","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"M\u00f6ller","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"Benning","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stanley","family":"Osher","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2012,6,7]]},"reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"M. 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