BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

Hybrid-Spline Dictionaries for Continuous-Domain Inverse Problems

T. Debarre, S. Aziznejad, M. Unser

IEEE Transactions on Signal Processing, vol. 67, no. 22, pp. 5824-5836, November 15, 2019.

We study one-dimensional continuous-domain inverse problems with multiple generalized total-variation regularization, which involves the joint use of several regularization operators. Our starting point is a new representer theorem that states that such inverse problems have hybrid-spline solutions with a total sparsity bounded by the number of measurements. We show that such continuous-domain problems can be discretized in an exact way by using a union of B-spline dictionary bases matched to the regularization operators. We then propose a multiresolution algorithm that selects an appropriate grid size that depends on the problem. Finally, we demonstrate the computational feasibility of our algorithm for multiple-order derivative regularization operators. 

@ARTICLE(http://bigwww.epfl.ch/publications/debarre1904.html,
AUTHOR="Debarre, T. and Aziznejad, S. and Unser, M.",
TITLE="Hybrid-Spline Dictionaries for Continuous-Domain Inverse
	Problems",
JOURNAL="{IEEE} Transactions on Signal Processing",
YEAR="2019",
volume="67",
number="22",
pages="5824--5836",
month="November 15,",
note="")

© 2019 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.