An image denoising algorithm using a physics-inspired deep image prior

Haridarshan Kumar and Sanjeev Kumar

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 246, issue C, 524-546

Abstract: Image denoising methods focus on noise removal with edge and texture preservation as the primary goal. Most deep learning methods are supervised in nature, i.e., they need noisy and clean image data to learn the mapping. On the contrary, deep image prior (DIP) is an unsupervised method. It works on the principle that a structured CNN with enough parameters can be used as the prior of the image. It captures noise with long training, which is a matter of concern. In this work, we try to resolve this problem of DIP. We incorporate the heat equation in DIP, as this equation has smoothing behavior, which is well known in the PDE-based image denoising community. For the validation, we perform the experiments on different images with Gaussian noise and speckle noise of varying levels. Additionally, a theoretical analysis of the mean squared error (MSE) progress over training iterations is presented for a deeper understanding of the training dynamics of both DIP and PI-DIP under these noise conditions. Experiments show that this strategy is not limited to specific noise. With this framework, we do not have to be concerned about the stopping point of DIP optimization, which is a great relief and has a greater impact on unseen image denoising problems.

Keywords: Deep image prior; Diffusion equation; Gaussian noise; Neural tangent kernel; Physics-informed neural networks; Speckle noise (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:246:y:2026:i:c:p:524-546

DOI: 10.1016/j.matcom.2026.01.032

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