Image denoising by generalized total variation regularization and least squares fidelity

Abstract

Inspired by the ability of $$\ell _p$$ l p -regularized algorithms and the close connection of total variation (TV) to the $$\ell _1$$ l 1 norm, a $$p$$ p th-power type TV denoted as TV $$_p$$ p is proposed for $$0\le p \le 1$$ 0 ≤ p ≤ 1 . The TV $$_p$$ p -regularized problem for image denoising is nonconvex thus difficult to tackle directly. Instead, we deal with the problem by proposing a weighted TV (WTV) minimization where the weights are updated iteratively to locally approximate the TV $$_p$$ p -regularized problem. The difficulty of WTV minimization is dealt with in a modified split Bregman framework. Numerical results are presented to demonstrate improved denoising performance of the new algorithm with $$p<1$$ p < 1 relative to that obtained by the standard TV minimization and several recent denoising methods from the literature on a variety of images.