Bayesian Sequential Optimal Experimental Design for Single-Pixel Imaging using Reinforcement Learning

Single-pixel sensing encodes a scene as a short sequence of coded measurements, and image-free methods infer the task directly from that sequence. We show that removing image reconstruction relocates the central design problem to the lift: how 1D measurements become a 2D task representation. We organize this choice as a lift spectrum from a fixed-physics inverse, through a learned static projection, to content-adaptive retrieval. These are not interchangeable forms of reconstruction: the fixed-physics route reconstructs an image consumed at inference, whereas our spatiotemporal soft-fusion (STSF) network lifts measurements directly into task features, and task-prioritized loss scheduling (TPLS) uses a separate learned reconstruction branch only as scheduled training supervision. A probe-selected recurrent encoder and a parameter-matched lift ablation identify the STSF design. In simulation, STSF+TPLS exceeds the prior image-free baseline on three datasets at 3.13% sampling (+3.2 to +9.9 pp foreground mIoU) and remains competitive down to 0.39%. The strongest clean-trained reconstruct-then-segment baseline wins without measurement noise, but measurement noise reverses the ranking: the reconstructed task input carries a 20-70x larger normalized relative perturbation than the measurements themselves. Stressed to failure, the three lift regions exhibit distinct dominant signatures--collapse, imprinting, and coarsening. STSF+TPLS transfers without fine-tuning to a real single-pixel bench, where the reversal reappears as a proof of concept; inference takes about 14 ms per mask on an RTX 4090. Within the tested fixed-acquisition regime, measurement-to-space adaptivity therefore organizes both the clean-to-noisy operating envelope and the failure a system encounters. Code and pretrained weights: https://github.com/Hanyuyuan6/STSF-TPLS.

Single-pixel imaging (SPI) is a promising imaging modality with distinctive advantages in strongly perturbed environments. Existing SPI methods lack physical sparsity constraints and overlook the integration of local and global features, leading to severe noise vulnerability, structural distortions and blurred details. To address these limitations, we propose SISTA-Net, a compressive sensing-inspired self-supervised method for single-pixel imaging. SISTA-Net unfolds the Iterative Shrinkage-Thresholding Algorithm (ISTA) into an interpretable network consisting of a data fidelity module and a proximal mapping module. The fidelity module adopts a hybrid CNN-Visual State Space Model (VSSM) architecture to integrate local and global feature modeling, enhancing reconstruction integrity and fidelity. We leverage deep nonlinear networks as adaptive sparse transforms combined with a learnable soft-thresholding operator to impose explicit physical sparsity in the latent domain, enabling noise suppression and robustness to interference even at extremely low sampling rates. Extensive experiments on multiple simulation scenarios demonstrate that SISTA-Net outperforms state-of-the-art methods by 2.6 dB in PSNR. Real-world far-field underwater tests yield a 3.4 dB average PSNR improvement, validating its robust anti-interference capability.

Despite offering high sensitivity, a high signal-to-noise ratio, and a broad spectral range, single-pixel imaging (SPI) is limited by low measurement efficiency and long data-acquisition times. To address this, we propose a wavelength-multiplexed, spatially incoherent diffractive optical processor combined with a compact/shallow digital artificial neural network (ANN) to implement compressive SPI. Specifically, we model the bucket detection process in conventional SPI as a linear intensity transformation with spatially and spectrally varying point-spread functions. This transformation matrix is treated as a learnable parameter and jointly optimized with a shallow digital ANN composed of 2 hidden nonlinear layers. The wavelength-multiplexed diffractive processor is then configured via data-free optimization to approximate this pre-trained transformation matrix; after this optimization, the diffractive processor remains static/fixed. Upon multi-wavelength illumination and diffractive modulation, the target spatial information of the input object is spectrally encoded. A single-pixel detector captures the output spectral power at each illumination band, which is then rapidly decoded by the jointly trained digital ANN to reconstruct the input image. In addition to our numerical analyses demonstrating the feasibility of this approach, we experimentally validated its proof-of-concept using an array of light-emitting diodes (LEDs). Overall, this work demonstrates a computational imaging framework for compressive SPI that can be useful in applications such as biomedical imaging, autonomous devices, and remote sensing.