TITLE:
Restoration of Multichannel Images by Nonlinear Parabolic Partial Differential Equations (PDEs) and Optimization by Convolutional Neural Networks (CNNs)
AUTHORS:
Konan Hyacinthe Kouassi, Goli Konan Charles Etienne, Diomande Moussa, Asseu Olivier
KEYWORDS:
Multichannel İmage Restoration, Partial Differential Equations (PDEs), Φ-Laplacian, Nonlinear Diffusion, Convolutional Neural Networks (CNNs), Image Denoising, PSNR, Deep Learning, Variational Models, Computer Vision
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.16 No.4,
April
30,
2026
ABSTRACT: Multichannel image restoration is a fundamental problem in image processing due to the unavoidable degradation introduced during acquisition, particularly Gaussian noise. In this article, we propose a hybrid approach combining a variational model based on nonlinear parabolic partial differential equations (PDEs) of the Φ-Laplacian type and a convolutional neural network (CNN) for color image denoising. The variational model ensures adaptive smoothing while preserving contours and fine structures through controlled nonlinear diffusion. In parallel, the CNN learns to reconstruct the clean image from the noisy image by exploiting the statistical regularities of the data. An experimental comparison is performed on images noisy with Gaussian noise, using the PSNR metric to evaluate the restoration quality. The results show that the Φ-Laplacian model significantly improves image quality (≈30.5 dB), while the CNN achieves superior performance (≈32 dB), with better visual reproduction. Analysis of the convergence curves highlights the stability of the proposed methods. Finally, the study underscores the value of a hybrid approach combining mathematical rigor and machine learning power.