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Storath, M.* ; Weinmann, A. ; Unser, M.*

Exact algorithms for L1-TV regularization of real-valued or circle-valued signals.

SIAM J. Sci. Comput. 38, A614-A630 (2016)
Open Access Green as soon as Postprint is submitted to ZB.
We consider L1-TV regularization of univariate signals with values on the real line or on the unit circle. While the real data space leads to a convex optimization problem, the problem is nonconvex for circle-valued data. In this paper, we derive exact algorithms for both data spaces. A key ingredient is the reduction of the infinite search spaces to a finite set of configurations, which can be scanned by the Viterbi algorithm. To reduce the computational complexity of the involved tabulations, we extend the technique of distance transforms to nonuniform grids and to the circular data space. In total, the proposed algorithms have complexity O(KN), where N is the length of the signal and K is the number of different values in the data set. In particular, the complexity is O(N) for quantized data. It is the first exact algorithm for total variation regularization with circle-valued data, and it is competitive with the state-of-the-art methods for scalar data, assuming that the latter are quantized.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Circle-valued Data ; Distance Transform ; Dynamic Programming ; Least Absolute Deviations ; Total Cyclic Variation ; Total Variation Regularization; Image-restoration; Reconstruction; Strings
ISSN (print) / ISBN 1064-8275
e-ISSN 1095-7197
Quellenangaben Volume: 38, Issue: 1, Pages: A614-A630 Article Number: , Supplement: ,
Publisher Society for Industrial and Applied Mathematics (SIAM)
Publishing Place Philadelphia
Reviewing status Peer reviewed