Training-free spectrum sampling strategy in Fourier single-pixel imaging via Deep Image Prior

Abstract

Fourier Single-pixel Imaging (FSI) reconstructs images by acquiring frequency domain information via a single-pixel detector. However, existing sampling strategies, whether predefined or data-driven, struggle to achieve a training-free, adaptive solution that balances efficiency with reconstruction quality. This paper proposes a novel training-free spectral sampling strategy based on Deep Image Prior (DIP) which is used for Fourier spectrum estimation to overcome the limitations of existing methods. By re-purposing DIP’s inpainting capability, the Fourier magnitude map is treated as an image to be inpainted, enabling adaptive, scene-specific estimation of the illumination order—without any external datasets or training. The approach leverages the structural equivalence between spatial and spectral domains and completes reconstruction using standard compressed sensing (CS) techniques. Experiments on natural and synthetic images demonstrate reconstruction performance gains over existing conventional and variable density sampling schemes, with up to 40% reduction in processing time compared to prior adaptive methods. Unlike existing methods, the proposed approach avoids redundant sampling, generalizes well across diverse image types, and remains entirely training-free.