Functional Lifting for Variational Problems with Higher-Order Regularization

Benedikt Loewenhauser, Jan Lellmann


Variational approaches are an established paradigm in the field of image processing. The non-convexity of the functional can be addressed by functional lifting and convex relaxation techniques, which aim to solve a convex approximation of the original energy on a larger space. However, so far these approaches have been limited to first-order, gradient-based regularizers such as the total variation. In this work, we propose a way to extend functional lifting to a second-order regularizer derived from the Laplacian. We prove that it can be represented efficiently and thus allows numerical optimization. We experimentally demonstrate the usefulness on a synthetic convex denoising problem and on synthetic as well as real-world image registration problems.

Original languageEnglish
Title of host publicationInternational Conference on Imaging, Vision and Learning based on Optimization and PDEs
PublisherSpringer Berlin Heidelberg
Publication date2018
Publication statusPublished - 2018


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