A data-driven algorithm for solving image despeckling PDE model using physics-informed ConvNet

• Published in: Computers & mathematics with applications (1987) Vol. 200; pp. 202 - 227
• Main Authors: Kumar, Haridarshan, Kumar, Sanjeev
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15.12.2025
• Subjects: Convolutional neural networks; Diffusion; Finite difference method; Image despeckling; PDEs; Physics-informed machine learning; Physics-informed machine learning; Convolutional neural networks; Diffusion; Image despeckling; PDEs; Finite difference method
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2025.09.022

In this study, we propose a new data-driven algorithm for the Perona-Malik image despeckling problem. The advantage of the proposed algorithm over neural network-based methods is that it does not need any noisy and clean image data pair for training. The proposed algorithm is implemented using a three-dimensional convolution neural network (ConvNet) architecture. We compare its output with results obtained from several existing methods, including the operator splitting RBF collocation method, the finite difference method (FDM), and physics-informed neural networks (PINNs). To evaluate the performance of the proposed algorithm, simulations are carried out using grayscale images that have been artificially corrupted with different levels of speckle noise. Using the peak signal to noise ratio (PSNR) and structural similarity index measure (SSIM) as the evaluation metric, we observed that the proposed algorithm outperforms these existing methods, demonstrating superior image quality with the same numerical scheme and the same discretization. To the best of our knowledge, this work represents the first application of physics-inspired convolutional neural network for PDE-based image despeckling model.