Abstract
Many applications show that nonconvex nonsmooth regularization has advantages for restoring images with neat edges. This phenomenon has been provided as a mathematical explanation for the anisotropic model through establishing a uniform lower bound for nonzero gradients of recovered images. For nonconvex and nonsmooth regularization using potential functions composed of the $\ell_2$ norm of the image gradient, i.e., the isotropic model, there lack reasonable theoretical results in the literature. Based on some properties of image gradient fields not considered previously, we obtain a uniform lower bound for the nonzero gradients of recovered images for the isotropic model, which implies the edge recovery property of this model. Our theoretical results are illustrated using a numerical experiment.
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