TY - JOUR
T1 - Image denoising: Learning the noise model via nonsmooth PDE-constrained optimization
AU - Reyes, Juan Carlos De los
AU - Schönlieb, Carola-Bibiane
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: Research partially supported by the Alexander von Humboldt Foundation. CBS acknowledges the financial support provided by the Cambridge Centre for Analysis (CCA), the Royal Society International Exchanges Award IE110314 for the project High-order Compressed Sensing for Medical Imaging, the EPSRC first grant Nr. EP/J009539/1 Sparse & Higher-order Image Restoration, and the EPSRC / Isaac Newton Trust Small Grant on Non-smooth geometric reconstruction for highresolution MRI imaging of fluid transport in bed reactors. Further, this publication is based on work supported by Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2013/11/27
Y1 - 2013/11/27
N2 - We propose a nonsmooth PDE-constrained optimization approach for the determination of the correct noise model in total variation (TV) image denoising. An optimization problem for the determination of the weights corresponding to different types of noise distributions is stated and existence of an optimal solution is proved. A tailored regularization approach for the approximation of the optimal parameter values is proposed thereafter and its consistency studied. Additionally, the differentiability of the solution operator is proved and an optimality system characterizing the optimal solutions of each regularized problem is derived. The optimal parameter values are numerically computed by using a quasi-Newton method, together with semismooth Newton type algorithms for the solution of the TV-subproblems. © 2013 American Institute of Mathematical Sciences.
AB - We propose a nonsmooth PDE-constrained optimization approach for the determination of the correct noise model in total variation (TV) image denoising. An optimization problem for the determination of the weights corresponding to different types of noise distributions is stated and existence of an optimal solution is proved. A tailored regularization approach for the approximation of the optimal parameter values is proposed thereafter and its consistency studied. Additionally, the differentiability of the solution operator is proved and an optimality system characterizing the optimal solutions of each regularized problem is derived. The optimal parameter values are numerically computed by using a quasi-Newton method, together with semismooth Newton type algorithms for the solution of the TV-subproblems. © 2013 American Institute of Mathematical Sciences.
UR - http://hdl.handle.net/10754/598555
UR - http://aimsciences.org//article/doi/10.3934/ipi.2013.7.1183
UR - http://www.scopus.com/inward/record.url?scp=84888390614&partnerID=8YFLogxK
U2 - 10.3934/ipi.2013.7.1183
DO - 10.3934/ipi.2013.7.1183
M3 - Article
SN - 1930-8337
VL - 7
SP - 1183
EP - 1214
JO - Inverse Problems and Imaging
JF - Inverse Problems and Imaging
IS - 4
ER -