Bilevel Parameter Learning for Higher-Order Total Variation Regularisation Models

• Published in: Journal of mathematical imaging and vision Vol. 57; no. 1; pp. 1 - 25
• Main Authors: De los Reyes, J. C., Schönlieb, C.-B., Valkonen, T.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.01.2017; Springer Nature B.V
• Subjects: Algorithms; Applications of Mathematics; Computer Science; Image Processing and Computer Vision; Image reconstruction; Learning; Mathematical analysis; Mathematical Methods in Physics; Noise levels; Optimization; Parameters; Regularization; Signal,Image and Speech Processing; Bilevel optimisation; Total variation regularisers; Image quality measures

We consider a bilevel optimisation approach for parameter learning in higher-order total variation image reconstruction models. Apart from the least squares cost functional, naturally used in bilevel learning, we propose and analyse an alternative cost based on a Huber-regularised TV seminorm. Diffe...