Abstract
This paper introduces a “directional total variation” (TV) where the gradients are weighted depending on their direction. The introduced directional TV has increased (and tunable) sensitivity to variations at a selected direction. In order to demonstrate the utility of the directional TV, we consider an image denoising formulation. This formulation requires the realization of the “proximal map” of the directional TV. Therefore, it is relevant for more general inverse problem settings as well. We derive an algorithm that solves the problem and use the algorithm to study the effects of the parameters of the directional TV.
Highlights
Total variation (TV) is a measure of the variations in an image
The denoising problem is equivalent to realizing the ‘proximal operator’ [1] associated with the proposed directional total variation, it can be useful in more general inverse problems formulations [1]–[3]
In order to demonstrate the utility of the proposed directional TV, experiments are performed with two images: 2 ‘wood’ (Fig. 1(a)) and ‘bamboo’ (Fig. 3(a))
Summary
Total variation (TV) is a measure of the variations in an image. It penalizes local changes in the image regardless of their direction. TV has proved its utility as a simple prior for piecewise smooth images with no globally dominant direction. We consider a variation of TV that provides a simple prior for such images. The denoising problem is equivalent to realizing the ‘proximal operator’ [1] associated with the proposed directional total variation, it can be useful in more general inverse problems formulations [1]–[3]
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