Multiplicative Gaussian Noise Removal using Partial Differential Equations and Activation Functions: A Robust and Stable Approach

Multiplicative noise poses challenges in image and signal processing due to its nonlinear and signal-dependent nature. Removing it while preserving information requires specialized techniques. We propose a novel approach for denoising images corrupted by multiplicative Gaussian noise using partial differential equations and activation functions. With a focus on learning the kernels, we address the crucial problem of denoising images with multiplicative noise, an area that has received relatively limited attention compared to additive noise. Our methodology leverages explicit schemes with a gray-level indicator matrix and explores various activation functions to improve denoising performance. Through extensive experimentation and evaluation, we achieved higher Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Indicator Measure (SSIM) values, thereby advancing the state-of-the-art in multiplicative noise removal.

Additional Keywords and Phrases: Image Denoising, Partial Differential Equations, Multiplicative Noise, ResNet, Gray Level Indicator.