Variable Exponent, Linear Growth Functionals in Image Restoration

Abstract

We study a functional with variable exponent, $1\leq p(x)\leq 2$, which provides a model for image denoising, enhancement, and restoration. The diffusion resulting from the proposed model is a combination of total variation (TV)-based regularization and Gaussian smoothing. The existence, uniqueness, and long-time behavior of the proposed model are established. Experimental results illustrate the effectiveness of the model in image restoration.