Improved total variation regularized physics-informed neural network for unsupervised image denoising
Abstract
Image denoising is a fundamental task in image processing, which directly affects the performance of subsequent tasks such as feature extraction and object recognition. Traditional total variation (TV) denoising models are effective in preserving edges but suffer from staircase effects, sensitivity to regularization parameters, and complex numerical solving. Existing Physics-Informed Neural Network (PINN) denoising methods often rely on specific physical constraints, which fail to optimize the image structure, leading to blurred edges and loss of detail. In this paper, we propose a new unsupervised image denoising method based on an improved TV constraint in PINNs. The method takes noisy images as input without requiring clean images as labels, and it achieves superior performance through four key innovations: 1) An improved TV constraint with an adaptive gradient smoothing factor and dynamic regularization parameter to alleviate staircase effects; 2) A generalized physical constraint based on the continuity of image grayscale values, eliminating dependence on specific physical equations; 3) A four-dimensional loss function combining data fidelity, physical consistency, edge preservation, and local variance, with an adaptive weight mechanism to balance the optimization priorities; 4) A two-stage training strategy with an adaptive deep multi-layer perceptron (AD-MLP) to balance convergence speed and model accuracy. Experiments on classic grayscale images with Gaussian noise (variance 0.01–0.05) demonstrate that the proposed method achieves a PSNR improvement of 2.1–5.3 dB, SSIM improvement of 0.06–0.18, and edge preservation index (EPI) improvement of 0.12–0.16, outperforming traditional TV models, pure PINN, Wiener filtering, adaptive TV, and two-stage fusion methods. It significantly mitigates staircase effects and shows superior denoising robustness, structural fidelity, and computational efficiency in complex noise environments.