Design of convolutional neural network-based layer operator for image denoising using fourth-order PDE

Images often suffer from speckle noise, which complicates processing. Conventional denoising methods are not effective in preserving the details of the images. This study proposes a novel approach for noise reduction in images, preserving complex structures. The process uses a diffusion network based on a fourth-order filtering partial differential equation (PDE). The PDE is transformed into a system of differential equations through finite difference methods, and a filtering layer operator is defined based on the discretized PDE and M-layer convolutional neural network (CNN). The CNN calculates denoising filters for the image at layer \(k-1\) $k-1$ , which are then applied to the diffusion network layer operator to update the appearance. Our proposed method has been tested on both BSD68 and ultrasound image datasets and produced improved denoising results compared to traditional methods.