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Adaptive Regularization for Image Reconstruction from Subsampled Data Read chapter Read first chapter

2018 | OriginalPaper | Chapter

5. Functional Lifting for Variational Problems with Higher-Order Regularization

Authors : Benedikt Loewenhauser, Jan Lellmann

Published in: Imaging, Vision and Learning Based on Optimization and PDEs

Publisher: Springer International Publishing

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Abstract

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.

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previous chapter Variational Methods for Gamut Mapping in Cinema and Television
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Footnotes
1
See [28] and http://​github.​com/​tum-vision/​prost for the most recent version.
 
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Metadata
Title
Functional Lifting for Variational Problems with Higher-Order Regularization
Authors
Benedikt Loewenhauser
Jan Lellmann
Copyright Year
2018
Book
Imaging, Vision and Learning Based on Optimization and PDEs

Print ISBN: 978-3-319-91273-8

Electronic ISBN: 978-3-319-91274-5

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-91274-5_5

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