{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,27]],"date-time":"2026-09-27T14:44:10Z","timestamp":1790520250714,"version":"4.1.0"},"reference-count":12,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2003,1]]},"abstract":"<jats:p>Many image processing applications require computing approximate solutions of very large, ill-conditioned linear systems. Physical assumptions of the imaging system usually dictate that the matrices in these linear systems have exploitable structure. The specific structure depends on (usually simplifying) assumptions of the physical model and other considerations such as boundary conditions. When reflexive (Neumann) boundary conditions are used, the coefficient matrix is a combination of Toeplitz and Hankel matrices. Kronecker products also occur, but this structure is not obvious from measured data. In this paper we discuss a scheme for computing a (possibly approximate) Kronecker product decomposition of structured matrices in image processing, which extends previous work by Kamm and Nagy [SIAM J. Matrix Anal. Appl., 22 (2000), pp. 155--172] to a wider class of image restoration problems.<\/jats:p>","DOI":"10.1137\/s0895479802419580","type":"journal-article","created":{"date-parts":[[2004,3,5]],"date-time":"2004-03-05T21:00:50Z","timestamp":1078520450000},"page":"829-841","source":"Crossref","is-referenced-by-count":48,"title":["Kronecker Product Approximations forImage Restoration with Reflexive Boundary Conditions"],"prefix":"10.1137","volume":"25","author":[{"given":"James G.","family":"Nagy","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael K.","family":"Ng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lisa","family":"Perrone","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","unstructured":"H. Andrews and B. Hunt,\n                      Digital Image Restoration\n                      , Prentice\u2010Hall, Englewood Cliffs, NJ, 1977."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1364\/AO.34.001859"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-1740-8"},{"key":"R4","unstructured":"R. Gonzalez and R. Woods,\n                      Digital Image Processing\n                      , Addison\u2010Wesley, Reading, MA, 1992."},{"key":"R5","unstructured":"D. Grishin and T. Strohmer,\n                      Fast multi\u2010dimensional scattered data approximation with Neumann boundary conditions\n                      , Linear Algebra Appl., to appear."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02149761"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719697"},{"key":"R8","unstructured":"A. K. Jain,\n                      Fundamentals of Digital Image Processing\n                      , Prentice\u2010Hall, Englewood Cliffs, NJ, 1989."},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479898345540"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(99)00274-8"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827598341384"},{"key":"R12","doi-asserted-by":"crossref","unstructured":"C. Van Loan, N. Pitsianis, Approximation with Kronecker products, NATO Adv. Sci. Inst. Ser. E Appl. Sci., Vol. 232, Kluwer Acad. Publ., Dordrecht, 1993, 293\u201331494j:65051","DOI":"10.1007\/978-94-015-8196-7_17"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0895479802419580","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:38:04Z","timestamp":1787333884000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0895479802419580"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,1]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2003,1]]}},"alternative-id":["10.1137\/S0895479802419580"],"URL":"https:\/\/doi.org\/10.1137\/s0895479802419580","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,1]]}}}