Image Denoising via Optimal Control of the Diffusivity Function in a PDE-constrained problem

Abstract

In this paper, we suggest a new picture denoising model for PDE-constrained problem that is based on the popular Perona-Malik model. We present a novel method based on the optimal control of the diffusivity function to overcome the staircasing effect and contrast loss, two intrinsic drawbacks of the Perona-Malik equation. Through adaptively controlling the diffusion process, our model successfully improves noise reduction while maintaining important image characteristics. Comparisons with some models show how much better our method is at preserving structural features and improving denoising performance.