Some Remarks on the Staircasing Phenomenon in Total Variation-Based Image Denoising

Abstract

This paper deals with the so-called staircasing phenomenon, which frequently arises in total variation-based denoising models in image analysis. We prove in particular that staircasing always occurs at global extrema of the datum and at all extrema of the minimizer. It is also shown that, for radial images, the staircasing always appears at the extrema and at the boundary of the image. We also prove the equivalence between the denoising model and the total variation flow, in the radial case, thus, extending a previous result in dimension one. This equivalence cannot hold in the non-radial case, as it is shown with a counterexample. This connection allows us to understand how the staircase zones and the discontinuities of the denoising problem evolve with the regularization parameter.