Binary-error compensation iteration for optimized Fourier single-pixel imaging

Fourier single-pixel imaging utilizing binary-speckles modulation offers significant advantages in high-speed acquisition; however, it is inherently constrained by quantization-induced image degradation. To address this challenge, we propose an optimized reconstruction method based on a binary-error compensation iterative framework. The approach implements an algorithmic heuristic based on the forward model of Fourier single-pixel imaging, which uses the initially binary-speckle reconstructed image as a dynamic reference to iteratively estimate and compensate for the otherwise unknown error spectrum during reconstruction. Specifically, an initial image is first reconstructed from binary-modulated signals to serve as a seed for subsequent refinement. This iterative loop systematically captures and compensates for the deviations between binary and gray-scale speckle responses, leveraging the estimated error spectrum to offset quantization-induced distortions. Both simulation and experimental results demonstrate that the proposed method enhances the imaging quality of conventional binary FSPI. By outperforming existing techniques, it effectively bridges the performance gap between binary modulation and high-fidelity grayscale Fourier single-pixel imaging.