Image denoising by generalized total variation regularization and least squares fidelity
Inspired by the ability of \(\ell _p\)-regularized algorithms and the close connection of total variation (TV) to the \(\ell _1\) norm, a \(p\)th-power type TV denoted as TV\(_p\) is proposed for \(0\le p \le 1\). The TV\(_p\)-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\(_p\)-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 \(p<1\) relative to that obtained by the standard TV minimization and several recent denoising methods from the literature on a variety of images.
image denoising tv wtv