TY - JOUR
T1 - A convergent overlapping domain decomposition method for total variation minimization
AU - Fornasier, M.
AU - Langer, A.
AU - Schönlieb, C.-B.
N1 - This article is published under an open access license.
PY - 2010/10
Y1 - 2010/10
N2 - In this paper we are concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of functionals formed by a discrepancy term with respect to the data and a total variation constraint. To our knowledge, this is the first successful attempt of addressing such a strategy for the nonlinear, nonadditive, and nonsmooth problem of total variation minimization. We provide several numerical experiments, showing the successful application of the algorithm for the restoration of 1D signals and 2D images in interpolation/inpainting problems, respectively, and in a compressed sensing problem, for recovering piecewise constant medical-type images from partial Fourier ensembles.
AB - In this paper we are concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of functionals formed by a discrepancy term with respect to the data and a total variation constraint. To our knowledge, this is the first successful attempt of addressing such a strategy for the nonlinear, nonadditive, and nonsmooth problem of total variation minimization. We provide several numerical experiments, showing the successful application of the algorithm for the restoration of 1D signals and 2D images in interpolation/inpainting problems, respectively, and in a compressed sensing problem, for recovering piecewise constant medical-type images from partial Fourier ensembles.
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-77957164123&partnerID=MN8TOARS
U2 - 10.1007/s00211-010-0314-7
DO - 10.1007/s00211-010-0314-7
M3 - Article
SN - 0945-3245
VL - 116
SP - 645
EP - 685
JO - Numerische Mathematik
JF - Numerische Mathematik
ER -