Deep learning informed diffusion equation model for image denoising

Image denoising is one of the fundamental problems in image processing. Convolutional neural network (CNN) based denoising approaches have achieved better performance than traditional methods, such as STROLLR and BM3D. However, CNNs can easily bring unexplainable artifacts to denoised images. In this article, a Deep Learning‐Informed Diffusion Equation (DLI‐DE) framework utilizing the image prior or the image gradient prior for image denoising is proposed. The image priors and gradient priors are learned from CNN models and used as coefficients in diffusion equations. The solution of DLI‐DE is infinitely smooth from the uniqueness of existence theorem, which guarantees that the denoised image is free of artifacts. Good properties of DLI‐DE also ensure high‐quality of denoising. The experimental analysis confirms that the denoising performance of DLI‐DE is comparable to that of contemporary CNN‐based denoising methods such as TNRD and DnCNN, while effectively preventing artifacts. The paper presents a Deep Learning Informed Diffusion Equation (DLI‐DE) framework for image denoising, which integrates CNN‐derived image priors into diffusion equations to avoid artifacts common with conventional CNN methods. The uniqueness of the DLI‐DE solution ensures artifact‐free and high‐quality denoising, with performance comparable to advanced CNN‐based methods.