A generalized Condat's algorithm of 1D total variation regularization

Artyom Makovetskii; Sergei Voronin; Vitaly Kober

doi:10.1117/12.2273618

19 September 2017 A generalized Condat's algorithm of 1D total variation regularization

Artyom Makovetskii, Sergei Voronin, Vitaly Kober

Proceedings Volume 10396, Applications of Digital Image Processing XL; 103962K (2017) https://doi.org/10.1117/12.2273618
Event: SPIE Optical Engineering + Applications, 2017, San Diego, California, United States

Abstract

A common way for solving the denosing problem is to utilize the total variation (TV) regularization. Many efficient numerical algorithms have been developed for solving the TV regularization problem. Condat described a fast direct algorithm to compute the processed 1D signal. Also there exists a direct algorithm with a linear time for 1D TV denoising referred to as the taut string algorithm. The Condat’s algorithm is based on a dual problem to the 1D TV regularization. In this paper, we propose a variant of the Condat’s algorithm based on the direct 1D TV regularization problem. The usage of the Condat’s algorithm with the taut string approach leads to a clear geometric description of the extremal function. Computer simulation results are provided to illustrate the performance of the proposed algorithm for restoration of degraded signals.

Citation Download Citation

Artyom Makovetskii, Sergei Voronin, and Vitaly Kober "A generalized Condat's algorithm of 1D total variation regularization", Proc. SPIE 10396, Applications of Digital Image Processing XL, 103962K (19 September 2017); https://doi.org/10.1117/12.2273618

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