Locally sparse reconstruction using the l1,∞-norm

Beitrag in einer Fachzeitschrift

Details zur Publikation

Autorinnen und Autoren: Heins P, Moeller M, Burger M
Zeitschrift: Inverse Problems and Imaging
Verlag: American Institute of Mathematical Sciences
Jahr der Veröffentlichung: 2015
Band: 9
Seitenbereich: 1093-1137
ISSN: 1930-8337
Sprache: Englisch


This paper discusses the incorporation of local sparsity information, e.g. in each pixel of an image, via minimization of the l1,∞-norm. We discuss the basic properties of this norm when used as a regularization functional and associated optimization problems, for which we derive equivalent reformulations either more amenable to theory or to numerical computation. Further focus of the analysis is put on the locally 1-sparse case, which is well motivated by some biomedical imaging applications. Our computational approaches are based on alternating direction methods of multipliers (ADMM) and appropriate splittings with augmented Lagrangians. Those are tested for a model scenario related to dynamic positron emission tomography (PET), which is a functional imaging technique in nuclear medicine. The results of this paper provide insight into the potential impact of regularization with the l1,∞-norm for local sparsity in appropriate settings. However, it also indicates several shortcomings, possibly related to the non-tightness of the functional as a relaxation of the l0,∞-norm.

Einrichtungen weiterer Autorinnen und Autoren

Technische Universität München (TUM)
Westfälische Wilhelms-Universität (WWU) Münster


Heins, P., Moeller, M., & Burger, M. (2015). Locally sparse reconstruction using the l1,∞-norm. Inverse Problems and Imaging, 9, 1093-1137. https://dx.doi.org/10.3934/ipi.2015.9.1093

Heins, Pia, Michael Moeller, and Martin Burger. "Locally sparse reconstruction using the l1,∞-norm." Inverse Problems and Imaging 9 (2015): 1093-1137.


Zuletzt aktualisiert 2018-04-12 um 09:08