Learned optical compression for single-pixel quantitative phase imaging

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.

Fourier phase encodes important spatial image structure, but recovering an image without measured spectral magnitude requires additional constraints and leaves absolute intensity ambiguous. We propose a projection-based two-stage framework that combines Fourier-phase and spatial-support constraints with an image-specific neural prior. The first stage alternates constraint enforcement with regularized neural-prior updates, while the second performs phase/support refinement alone with guaranteed convergence. We evaluate two neural-prior implementations on the same 77 microscopy images and compare them with a constraint-only baseline. After 500 final refinement passes, the best-performing variant achieves 31.41 dB pooled PSNR, 35.75 dB mean PSNR, and 0.9531 mean SSIM, improving pooled PSNR by 1.51~dB and reducing pooled MSE by 29.3% relative to the baseline. The results demonstrate the benefit of combining neural guidance with explicit constraint refinement at the evaluated iteration budget, while showing that lower phase residual alone does not guarantee greater reconstruction accuracy.

Adaptive compressed sensing (CS) aims to select the most informative measurements sequentially, which is crucial for many modern imaging systems. This task can be formulated as a Bayesian sequential optimal experimental design (sOED) problem, where each new acquisition is chosen to maximally reduce uncertainty about the unknown image given prior information and subsequent data provided by acquisitions. However, in single-pixel imaging (SPI), the large design space consists of all possible binary illumination patterns. Directly optimizing the Bayesian sOED objective over this space using conventional methods is generally challenging. In this work, we reformulate sOED for SPI as a reinforcement learning (RL) problem. In RL, an agent learns a policy through repeated experimental trials to maximize a reward, here given as the expected information gain, the most complete measure of uncertainty reduction in Bayesian OED. This avoids the need to directly optimize complex information-theoretic objectives during a measurement to obtain the next design. Instead, the result is a learned policy function that directly maps the current posterior belief about the image to the next optimal binary measurement pattern, in a computationally efficient way. Using a simple yet representative SPI imaging scenario, this work evaluates the scalability of the learned policy under two different policy parameterizations. Furthermore, we investigate how performance deteriorates when only approximate posterior information is available or the measurements are impaired by noise, and propose several strategies to introduce additional design constraints motivated by biomedical applications. The numerical experiments demonstrate that the proposed Bayesian sOED-RL framework remains robust and can be extended to more complex, large-scale SPI scenarios.