An efficient algorithm of 3D total variation regularization
Artyom Makovetskii, Сергей Воронин, Vitaly Kober · 2018
One of the most known techniques for signal and image denoising is based on total variation regularization (TV regularization). There are two known types of the discrete TV norms: isotropic and anisotropic. One of the key difficulties in the TV-based image denoising problem is the nonsmoothness of the TV norms. Many properties of the TV regularization for 1D and 2D cases are well known. On the contrary, the multidimensional TV regularization, basically, an open problem. In this work, we deal with TV regularization in the 3D case for the anisotropic norm. The key feature of the proposed method is to decompose the large problem into a set of smaller and independent problems, which can be solved efficiently and exactly. These small problems are can be solved in parallel. Computer simulation results are provided to illustrate the performance of the proposed algorithm for restoration of degraded data.