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Reordering for improving global Arnoldi-Tikhonov method in image restoration problems
Azarbaijan Shahid Madani Univ, Dept Appl Math, Tabriz, Iran..
Azarbaijan Shahid Madani Univ, Image Proc Lab, Tabriz, Iran..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-1118-6483
2018 (English)In: Signal, Image and Video Processing, ISSN 1863-1703, E-ISSN 1863-1711, Vol. 12, no 3, p. 497-504Article in journal (Refereed) Published
Abstract [en]

This paper discusses the solution of large-scale linear discrete ill-posed problems arising from image restoration problems. Since the scale of the problem is usually very large, the computations with the blurring matrix can be very expensive. In this regard, we consider problems in which the coefficient matrix is the sum of Kronecker products of matrices to benefit the computation. Here, we present an alternative approach based on reordering of the image approximations obtained with the global Arnoldi-Tikhonov method. The ordering of the intensities is such that it makes the image approximation monotonic and thus minimizes the finite differences norm. We present theoretical properties of the method and numerical experiments on image restoration.

Place, publisher, year, edition, pages
Springer London, 2018. Vol. 12, no 3, p. 497-504
Keywords [en]
Inverse problems, Regularization methods, Reordering, Kronecker product
National Category
Signal Processing
Identifiers
URN: urn:nbn:se:kth:diva-240178DOI: 10.1007/s11760-017-1185-5ISI: 000426815900013Scopus ID: 2-s2.0-85030860938OAI: oai:DiVA.org:kth-240178DiVA, id: diva2:1272617
Note

QC 20181218

Available from: 2018-12-19 Created: 2018-12-19 Last updated: 2022-06-26Bibliographically approved

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Öktem, Ozan

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