Weighted and Well-Balanced Nonlinear TV-Based Time-Dependent Model for Image Denoising

Abstract

The partial differential equation (PDE)-based models are widely used to remove additive Gaussian white noise and preserve edges, and one of the most widely used methods is the total variation denoising algorithm. Total variation (TV) denoising algorithm-based time-dependent models have seen considerable success in the field of image-denoising and edge detection. TV denoising algorithm is based on that signals with spurious detail have a high total variation and reduction of unwanted signals to achieve noise-free images. It is a constrained optimization-type algorithm. The Lagrange multiplier and gradient descent method are used to solve the TV algorithm to reach the PDE-based time dependent model. To eliminate additive noise and preserve edges, we investigate a class of weighted time-dependent model in this study. The proposed method is investigated in a well-balanced flow form that extends the time-dependent model with an adaptive fidelity element. Adaptive function is fusing into the regularization term of the classical time-dependent model which successfully enhances the intensity of the regularizer function. We maintain the ability of the time-dependent model without any oscillation effects. Furthermore, we want to prove the viscosity solution of our weighted and well balanced time-dependent model, demonstrating its existence and uniqueness. The finite difference method is applied to discretize the nonlinear time-dependent models. The numerical results are expressed as a statistic known as the peak signal-to-noise ratio (PSNR) and structural similarity index metric (SSIM). Numerical experiments demonstrate that the proposed model yields good performance compared with the previous time-dependent model.

Keywords

• partial differential equation
• total variation
• time dependent model
• weighted and well balanced
• image denoising
• image smoothing
• viscosity solution
• explicit scheme