Tensor-guided learning for image denoising using anisotropic PDEs

Abstract

In this article, we introduce an advanced approach for enhanced image denoising using an improved space-variant anisotropic Partial Differential Equation (PDE) framework. Leveraging Weickert-type operators, this method relies on two critical parameters: \(\lambda \) and \(\theta \), defining local image geometry and smoothing strength. We propose an automatic parameter estimation technique rooted in PDE-constrained optimization, incorporating supplementary information from the original clean image. By combining these components, our approach achieves superior image denoising, pushing the boundaries of image enhancement methods. We employed a modified Alternating Direction Method of Multipliers (ADMM) procedure for numerical optimization, demonstrating its efficacy through thorough assessments and affirming its superior performance compared to alternative denoising methods.