A fast one dimensional total variation regularization algorithm

Abstract

Denoising has numerous applications in communications, control, machine learning, and many other fields of engineering and science. A common way to solve the problem utilizes 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. 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 method with the taut string approach leads to a clear geometric description of the extremal function.