Communications in Mathematical Sciences
Volume 20 (2022)
Adaptive image processing: A bilevel structure learning approach for mixed-order total variation regularizers
Pages: 1117 – 1149
We propose a class of mixed-order PDE-constraint regularizer for image processing problem, generalizing the standard first-order total variation (TV). Then, we study the corresponding semi-supervised (bilevel) training scheme, which provides a simultaneous optimization with respect to parameters and new class of regularizers. Finally, by relying on the finite approximation method, we solve the global optimization problem on such training scheme, and analyze the resulting numerical results.
image processing, optimal training scheme, higher-order differential operators, $\Gamma$-convergence
2010 Mathematics Subject Classification
26B30, 47J20, 94A08
P. Liu acknowledges support from the EPSRC Centre Nr. EP/N014588/1 and the Leverhulme Trust project on Breaking the non-convexity barrier.
X.Y. Lu acknowledges the support of his NSERC Discovery Grant “Regularity of minimizers and pattern formation in geometric minimization problems”.
Received 27 April 2021
Received revised 30 October 2021
Accepted 30 October 2021
Published 11 April 2022