Fourier Single-Pixel Imaging Based on Wavelet Decomposition and Diffusion Model

Abstract

High-quality image reconstruction at low sampling rates remains a key challenge in Fourier single-pixel imaging (FSPI). To address the issue of image blur caused by the lack of high-frequency components in FSPI images under low sampling rates, a Frequency Constraint and Wavelet decomposition Diffusion Model (FC-WDM) method for Fourier single-pixel imaging is proposed. The image is first decomposed via wavelet transform into one low-frequency sub-band and three high-frequency sub-bands. The proposed method designs targeted recovery strategies for the low-frequency and high-frequency sub-bands, respectively. For the low-frequency sub-band reconstruction, a conditional diffusion model is employed. For the high-frequency sub-bands, a deep Fourier module (DFM-Block) is specially designed for image reconstruction. To overcome the bottleneck of traditional convolution, which is limited by a local receptive field, the deep Fourier module incorporates a dedicated frequency-domain filter block after spatial feature extraction. Specifically, this module maps the feature maps to the frequency domain using the fast Fourier transform (FFT) and achieves global receptive field coverage in the spatial domain by performing joint convolution on both the real and imaginary parts. Additionally, a frequency physical constraint module is designed to ensure that the model generation process remains anchored to the actual observed information. Both simulation and real-world experimental results confirm that the proposed network significantly improves the quality of image reconstruction at low measurement rates.