19 September 2017 A generalized Condat's algorithm of 1D total variation regularization
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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.
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Artyom Makovetskii, Sergei Voronin, 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); doi: 10.1117/12.2273618; https://doi.org/10.1117/12.2273618

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