- The paper presents SISTA-Net, a novel framework that unrolls ISTA to integrate physics-informed modules with deep learning for single-pixel imaging.
- The paper demonstrates significant PSNR and SSIM improvements over state-of-the-art methods at ultra-low sampling ratios, underscoring its reconstruction fidelity.
- The paper achieves robust performance in simulated and real-world underwater experiments, proving the model's adaptive sparsity and noise suppression capabilities.
Compressive Sensing-Inspired Self-Supervised Single-Pixel Imaging (SISTA-Net)
Introduction
"Compressive sensing inspired self-supervised single-pixel imaging" (2603.29732) presents SISTA-Net, a novel computational imaging framework that unifies model-based compressive sensing (CS), self-supervised deep learning, and a physically grounded architectural composition for single-pixel imaging (SPI). SPI, which reconstructs spatial scenes from scalar measurements via a modulated light field, is especially relevant for imaging in highly perturbed media or severely photon-limited scenarios. The core challenge is extracting high-fidelity reconstructions from strongly compressed and noisy measurements, highlighting the need for both robust sparsity priors and interpretable learning-based architectures immune to label scarcity.
Methodology
SISTA-Net Architecture
SISTA-Net directly unfolds the iterative shrinkage-thresholding algorithm (ISTA), defining an interpretable, physics-informed network comprised of two decoupled modules:
- Data Fidelity Module: Implemented via a custom CNN-VSSM hybrid, this module ensures explicit measurement consistency while balancing local and nonlocal structural modeling. The architecture, Res2MM-Net, fuses multi-receptive CNN blocks, residual connections, and hierarchical visual state space modeling (VSSM) via window partitioning (WinMamba blocks) for efficient local-global feature synthesis. This design overcomes the locality limitations of standard convolutions and the spatial corruption by naive sequence modeling, optimally extracting both fine-scale and global texture information.
- Proximal Mapping Module: Uniquely, non-linear deep encoders replace hand-crafted linear transforms for adaptive sparse feature projection, followed by a learnable soft-thresholding operator. A mirrored decoder reconstructs the image estimate, enforcing structural sparsity and explicit noise suppression within the latent domain. The operator design leverages smoothed soft-thresholding with physically constrained adaptive parameters, ensuring effective gradient flow during optimization and continuous enforcement of sparsity.
Losses and Self-Supervision
Training is strictly self-supervised, relying only on 1D measurement signals, and completely bypasses the need for paired datasets. The composite loss comprises:
- A fidelity term (MSE) for measurement consistency,
- An l1​ sparsity term on thresholded latent features,
- A KL-divergence-based proximal loss leveraging softmaxed measurement and simulation vectors to mitigate collapse and strutural degradation.
This ensures robust convergence and physical interpretability of learned representations, directly encoding the physics of SPI.
Experimental Results
Simulation Studies
Extensive simulation on binary and complex grayscale images (size 320×320) demonstrates that SISTA-Net consistently surpasses state-of-the-art baselines, including DGI, SwinIR, Restormer, DnCNN, and UNet.
- At ultra-low sampling ratios (as low as 0.97%), SISTA-Net reconstructs recognizable image structure, in stark contrast to the patchy, artifact-laden reconstructions of comparators.
- Quantitative metrics confirm improvements: On binary images, SISTA-Net achieves a mean PSNR gain of 2.6 dB over the next-best competitor, and SSIM is consistently higher, especially at low sample rates.
- In difficult detail recovery tasks (such as dense fine stripes), vertical grayscale cross-sections of SISTA-Net outputs are sharply aligned to ground truth, highlighting the model’s superior high-frequency structure preservation and noise rejection capabilities.
Adaptivity to Sampling Ratio
SISTA-Net exhibits a pronounced performance gap over competitors specifically at extreme undersampling ratios, with this gap narrowing as sampling increases, validating its true CS nature. SSIM and PSNR curves are monotonically increasing with sample count; SISTA-Net's PSNR is always highest, maintaining structural integrity and minimal background noise, demonstrating both robustness and sampling efficiency.
Underwater Real-World Experiments
The framework’s generalization is validated through real-world far-field underwater SPI, at propagation distances up to 52 meters. The SPI setup integrates modulated laser illumination, a rotating diffuser, and far-field target reflectors, with 1D measurements captured via a single-photon detector.
- SISTA-Net yields a 3.4 dB PSNR uplift and significant enhancement in contrast-to-noise ratio (CNR) compared to baselines.
- Critically, severe noise, scattering, and environmental perturbations debilitate all alternative methods, which exhibit pronounced artifacts, signal loss, and structural infidelity.
- SISTA-Net uniquely maintains sharp boundaries, structural integrity, and minimal background noise, directly attributable to latent-domain sparsity enforcement and measurement-constrained learning.
Ablation Studies
Comprehensive ablations confirm the necessity of each core module and loss component:
- Exclusion of the proximal mapping module leads to significant PSNR drops, reaffirming the role of learnable latent sparsity.
- Replacement of hybrid convolutional-state space feature extractors with simple convolutions diminishes detail retention and noise suppression.
- Loss ablations demonstrate that each term is indispensable for the architectural synergy required for high-quality, physically consistent SPI.
Theoretical and Practical Implications
The work establishes that physically interpretable, CS-inspired deep architectures can be merged with self-supervised learning to achieve high-fidelity SPI, even under strict sampling and real-world physical constraints. The hybrid CNN-VSSM design suggests that windowed state-space models surpass self-attention for tasks with strong local priors, particularly within the DIP paradigm.
By fully eliminating dataset dependence and enforcing domain-consistent sparse priors, SISTA-Net provides a route toward operational SPI in environments previously inaccessible to either analytic or data-driven approaches. This sets a precedent for future inverse problems in computational imaging, especially where labels are scarce and noise/interference are dominant.
Future Directions
Potential advances may extend to:
- Scalable, hardware-in-the-loop SPI systems leveraging SISTA-like architectures for real-time, in situ imaging.
- Expansion of the proximal mapping module to handle additional physical constraints relevant to various imaging modalities (e.g., phase retrieval, multispectral SPI).
- Extension to more general unrolled architectures that integrate adaptive physics-based regularization with self-supervised paradigms for a broader class of inverse problems.
- Investigation of hybrid windowed state-space and attention models for multimodal image reconstruction in turbulent or scattering environments.
Conclusion
SISTA-Net marks a substantial step forward in SPI, integrating interpretable, physics-constrained deep unrolling networks with adaptive latent sparsity and self-supervised learning. It achieves state-of-the-art reconstruction fidelity under extreme sampling and noise, robust generalization to physically challenging environments, and sets a solid foundation for future advances in self-supervised, domain-consistent computational imaging.