K-FISTA: a Kronecker-domain FISTA unrolling network for flexible single-pixel imaging across sampling ratios and multiple image resolutions.

Single-pixel imaging (SPI) has attracted considerable attention due to its simple hardware architecture and broad spectral adaptability. However, achieving high-quality SPI reconstruction that robustly adapts to varying sampling ratios and multiple image resolutions remains a challenge. To address this, we propose K-FISTA, a Kronecker-domain fast iterative shrinkage-thresholding algorithm (FISTA) unrolling network for flexible SPI reconstruction. The proposed framework follows a FISTA-inspired unrolling paradigm under the Kronecker compressed sensing model and reformulates momentum extrapolation, gradient descent, and prior modeling as learnable modules. Specifically, a tensor-form gradient descent step enforces measurement fidelity directly in the two-dimensional image domain, avoiding the construction of large-scale vectorized sensing matrices. A cross-stage state momentum refinement (CSMR) module adaptively exploits historical reconstruction information, while a deep restoration prior equipped with multi-branch global modeling and channel attention calibration enhances structural and textural recovery. Additionally, an explicit restoration target supervision strategy is introduced to guide progressive reconstruction across unfolding stages. Extensive simulated and real-world experiments demonstrate that K-FISTA enables accurate, efficient, and flexible SPI reconstruction using a single trained model across sampling ratios from 1% to 50% and multiple image resolutions, including 128 × 128, 256 × 256, 321 × 481, and 512 × 512. Notably, on the Set11 dataset, K-FISTA obtains PSNR/SSIM values of 22.93 dB/0.6426 at a 1% sampling ratio and 28.33 dB/0.8475 at a 4% sampling ratio, highlighting its robustness in severely undersampled regimes and practical adaptability to varying acquisition settings.