The Shannon Total Variation

Discretization schemes commonly used for total variation regularization lead to images that are difficult to interpolate, which is a real issue for applications requiring subpixel accuracy and aliasing control. In the present work, we reconciliate total variation with Shannon interpolation and study a Fourier-based estimate that behaves much better in terms of grid invariance, isotropy, artifact removal and subpixel accuracy. We show that this new variant (called Shannon total variation) can be easily handled with classical primal–dual formulations and illustrate its efficiency on several image processing tasks, including deblurring, spectrum extrapolation and a new aliasing reduction algorithm.