Poisson Denoising Variational Model Based on Prior-Driven Deep Neural Network

Abstract

The denoising of Poisson noise images is a typical ill-conditioned inverse problem. Its variational model requires repeated iterations and parameter adjustments, which is less computationally efficient. Pure deep learning models often draw on experience to design networks, but they have poor interpretability. Based on the Alternating Direction Method of Multipliers(ADMM) expansion of the Poisson noise denoising variational model, an end-to-end Deep Convolutional Neural Network(DCNN) is designed to derive an improved Poisson denoising variational model by combining the Poisson noise distribution data with the Bayesian maximum a posteriori probability estimation. To solve the Poisson denoising energy function extremum problem, ADMM is used, which introduces auxiliary variables, Lagrange multipliers, and penalty parameters and decomposes the problem into two alternating optimization subproblems of Gaussian denoising and image reconstruction. First, Gaussian denoising is achieved using the priori-driven DCNN to learn the Gaussian denoising. Next, the image reconstruction is completed via analytical iteration. The experimental results show that compared with the NonLinear Principal Component Analysis(NLPCA), VST+BM3D, I+VST+BM3D, and TRDPD-based Poisson denoising models, the mean values of the Peak Signal-to-Noise Ratio(PSNR) of the model on the Set12 dataset are improved by 2.73, 0.87, 0.57, and 0.50 dB, respectively, and the mean values of the Structural SIMilarities(SSIM) are improved by 0.148, 0.046, 0.020, and 0.047, respectively. The Poisson denoising effects on color images and Positron Emission Tomography/Computed Tomography(PET/CT) images are significantly improved. The above experimental results prove that the model effectively removes the Poisson noise and prevents the problems of artifacts and scattering generated during the Poisson denoising process.