Hybrid++: The Bridge between PDE Models and Deep Learning for Gamma Noise Removal

Abstract

Multiplicative gamma noise is one of the dominant noise factors in Synthetic Aperture Radar (SAR) and medical ultrasound images. They are dependent on pixel level noises due to which they are highly varying across the image and harder to handle as compared to additive noise. The denoising methods to address this noise currently include classical partial differential equation (PDE) methods which are good for interpretation but lack the restoration ability as compared to the state-of-the-art models while deep convolutional networks like DnCNN achieve high performance but at the cost of transparency due to which practitioners are skeptical to use them in high-risk critical fields like medicine. This paper presents Hybrid++, a novel trainable nonlinear reaction-diffusion architecture that addresses both the concerns - staying interpretable while offering performance close to huge black-box models. It combines a fully learnable PDE initialization with a 3-stage reaction-diffusion network having 64-channel multiscale filter banks, 4-layer Squeeze-and-Excitation attention-based influence functions and a 64-dimensional noise level embedding. It uses a two-phase training strategy, stage-wise optimization followed by joint end-to-end refinement which enables co-adaptation of all learnable parameters. On the FoE benchmark, Hybrid++ substantially improves over classical PDE, BM3D and the original TNRD baselines. In the severe-noise setting L=1, it comes within 0.23 dB PSNR of a separately trained DnCNN while using only about 8% of its parameters. We therefore position Hybrid++ not as a universal state-of-the-art image restoration backbone, but as a compact, physically structured reaction-diffusion model for multiplicative gamma noise.