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Discrete Total Variation Model with Gradient Fidelity Term for Image Restoration

In this paper, we introduce a new discrete model for image denoising. We first smooth the gradient field of the observed image by a discrete total variation model. Then we construct a new discrete functional with the smoothed gradient fidelity term, which can alleviate the staircasing effect efficiently and preserve sharp discontinuities during the images denoising. Here, the difference discrete variation principle is used to get the discrete Euler-Lagrange equation. We also discuss some numerical experiments which prove our proposed model and algorithms to be more efficient. In this paper, we introduce a discrete total variation model on the lattice, which is derived from the ideas of total variation minimization model. Then we propose a new discrete model for image denoising with discrete gradient fidelity term. At first, we smooth the gradient field of the observed image by discrete total variation model. Then we construct a new discrete functional with the smoothed gradient fidelity term, which helps to alleviate the staircasing effect efficiently and preserve sharp discontinuities in images. Here, the difference discrete variation principle is used for getting the discrete Euler-Lagrange equation. This paper is organized as follows. In Section 2, we intro- duce the discrete total variation model and give the method to get the value of the parameter. In Section 3, A two-step method model is proposed based on discrete total variation model, which is a discrete total variation model with gradient fidelity term. In Section 4, some numerical experiments are given to show the performance and effectiveness of our method. A brief summary is presented at the end of the paper. II. DISCRETE TOTAL VARIATION MODEL