The digital TV filter and nonlinear denoising

Motivated by the classical TV (total variation) restoration model, we propose a new nonlinear filter - the digital TV filter for denoising and enhancing digital images, or more generally, data living on graphs. The digital TV filter is a data dependent lowpass filter, capable of denoising data without blurring jumps or edges. In iterations, it solves a global total variational (or L ¹) optimization problem, which differs from most statistical filters. Applications are given in the denoising of one-dimensional (1-D) signals, two-dimensional (2-D) data with irregular structures, gray scale and color images, and nonflat image features such as chromaticity.