An efficient algorithm of total variation regularization in the two-dimensional case

Abstract

Denoising has numerous applications in communications, control, machine learning, and many other fields of engineering and science. Total variation (TV) regularization is a widely used technique for signal and image restoration. There are two types of TV regularization problem: anisotropic TV and isotropic TV. One of the key difficulties in the TV-based image denoising problem is the nonsmoothness of the TV norms. There are known exact solutions methods for 1D TV regularization problem. Strong and Chan derived exact solutions to TV regularization problem for onedimensional case. They obtained the exact solutions when the original noise-free function, noise and the regularization parameter are subject to special constraints. Davies and Kovac considered the problem as non-parametric regression with emphasis on controlling the number of local extrema, and in particular consider the run and taut string methods. Condat proposed a direct fast algorithm for searching the exact solutions to the one-dimensional TV regularization problem for discrete functions. In the 2D case, some methods are used to approximate exact solutions to the TV regularization problem. In this presentation, we propose a new approximation method for 2D TV regularization problem based on the fast exact 1D TV approach. Computer simulation results of are presented to illustrate the performance of the proposed algorithm for the image restoration.