Image denoising by generalized total variation regularization and least squares fidelity

Inspired by the ability of $$\ell _p$$ℓp-regularized algorithms and the close connection of total variation (TV) to the $$\ell _1$$ℓ1 norm, a $$p$$pth-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.

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