Complete Collection of Partial Differential Equation-Based Image Denoising Algorithms with MATLAB Implementation

This document provides a complete collection of partial differential equation (PDE)-based image denoising algorithms implemented in MATLAB. The collection includes working code implementations for the Perona-Malik anisotropic diffusion model (commonly known as PM equation) and shock filter algorithms. These sophisticated mathematical approaches enable effective noise removal from digital images, resulting in cleaner, sharper images that are more suitable for analysis and interpretation. The MATLAB implementations feature robust numerical methods for solving PDEs, including finite difference schemes for spatial discretization and appropriate time-stepping methods. The PM equation implementation employs gradient-based diffusion control using edge-stopping functions to preserve important image features while removing noise. The shock filter algorithm utilizes morphological operations through PDE formulations to enhance edges and reduce noise simultaneously. By utilizing these code implementations, researchers and practitioners can perform various image processing and optimization tasks, achieving superior results in image restoration and enhancement applications. Each algorithm includes parameter tuning options allowing users to customize the denoising strength and feature preservation according to specific application requirements.