WDBDM: Wavelet-based dual-branch diffusion model for low-dose CT and PET denoising

X-ray computed tomography (CT) and positron emission tomography (PET) are imaging modalities for assessing various diseases. While normal-dose CT (NDCT) and normal-dose PET (NDPET) imaging ensure high image quality, they often raise concerns regarding potential health risks from radiation exposure. This contradiction between reducing radiation dose and preserving diagnostic performance can be effectively addressed by reconstructing low-dose CT and low-dose PET images into high-quality images comparable to their normal-dose counterparts. In this study, we present WDBDM, a wavelet-based dual-branch diffusion framework for denoising low-dose data to generate normal-dose quality images. WDBDM consists of four main parts: Discrete Wavelet Transform (DWT), Low-Frequency Diffusion Branch (LFDB), High-Frequency Diffusion Branch (HFDB) and Fusion Module. Furthermore, we investigate the effectiveness of the Fusion Spatial–Frequency Convolution Module (FSFCM) in the diffusion branch, which can jointly extract spatial and frequency domain information, thereby significantly enhancing the feature representation capability of the model. Moreover, to prevent error propagation from imperfect recovery operators and to enable bidirectional guidance across high- and low-frequency components during sampling, we integrate HLF-MEMNet, a novel recovery network, into the WDBDM framework. This network leverages contextual information and high-low frequency mutual guidance constraints during the sampling process, preventing structural distortion and ensuring better alignment with the input at the next time step. Experiments on four public datasets and two imaging modalities demonstrate that WDBDM outperforms existing methods in denoising performance and generalization ability.