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Proximal Algorithm Unrolling: Flexible and Efficient Reconstruction Networks for Single-Pixel Imaging
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Proposes ProxUnroll, an HQS/ADMM unrolling framework for single-pixel imaging that trains a CNN-Transformer deep image restorer with a proximal trajectory loss so it approximates the proximal operator of an explicit restoration regularizer, giving one model that works across compression ratios.
Problem
Single-pixel imaging reconstruction: PnP methods flexibly handle varying compression ratios but are less accurate and slower, while unrolling networks are accurate and fast but must be retrained for each compression ratio.
Approach
Train unrolled HQS/ADMM networks with a proximal trajectory (PT) loss that aligns each unrolled iterate with the trajectory of an ideal explicit restorer (distance-to-ground-truth regularizer), so the learned deep image restorer approximates a proximal operator and generalizes across CRs; the DIR combines a memory block (channel cross-attention across iterations), a CNN-Transformer block (Swin + g
Key results
- HQS-ProxUnroll and ADMM-ProxUnroll reach average PSNR 32.55 and 32.59 dB on Set11 across CRs 0.01-0.50 with a single model, above HATNet (32.41) and other CR-specific unrolling networks.
- On BSD68 the ADMM variant averages 30.50 dB, versus 30.31 for SAUNet and 28.83 for PnP-DRUNet.
- At CR 0.25 on 256x256 images, ProxUnroll uses 107.73 GMACs, 3.90M params and 0.27 s runtime, versus 494.42 GMACs and 0.60 s for HATNet.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ADMM-ProxUnroll instead of HATNet | SPI reconstruction · Set11 (average) | PSNR: 32.41 -> 32.59 | Helped |
| Use ADMM-ProxUnroll instead of HATNet | SPI reconstruction · Set11 (average) | SSIM: 0.8640 -> 0.8692 | Helped |
| Use ADMM-ProxUnroll instead of SAUNet | SPI reconstruction · BSD68 (average) | PSNR: 30.31 -> 30.50 | Helped |
| Use ADMM-ProxUnroll instead of SAUNet | SPI reconstruction · BSD68 (average) | SSIM: 0.7951 -> 0.8046 | Helped |
| Add ChanCA to the DIR (ablation) | HQS-ProxUnroll · Set11, CR = 0.10 | PSNR: 31.42 -> 32.51; 1.09 dB | Helped |
| Use SwinT instead of a CNN, without doubling GD-CNN channel capability (ablation) | HQS-ProxUnroll DIR · Set11, CR = 0.10 | PSNR: 32.25 -> 32.51; 0.26 dB | Helped |
| Use AdaConv instead of one depth-wise convolution (ablation) | HQS-ProxUnroll DIR · Set11, CR = 0.10 | PSNR: 32.36 -> 32.51; 0.15 dB | Helped |
| Train with proximal trajectory loss instead of regular MSE loss (ablation) | HQS/ADMM-ProxUnroll · SPI reconstruction convergence | PSNR | Helped |
| Replace proximal trajectory loss with regular MSE loss (ablation) | HQS/ADMM-ProxUnroll · SPI reconstruction convergence | PSNR | Hurt |
Surprising findings
- Intermediate outputs of prior unrolling networks (SAUNet, HATNet) follow twisted, non-monotone trajectories, and reducing their intermediate artifacts made final outputs worse.
Limitations
- Unrolling with fixed number of iterations (6) limits flexibility to iteration count choice
- Proximal convergence guarantees are asserted via the trajectory loss rather than proven for the learned operator
- Real-data evaluation is limited to a single resolution target example
Experimental setup
Datasets: BSD500
Benchmarks: Set11 BSD68 real captured SPI data (resolution target)
Metrics: PSNR SSIM MACs Params runtime
Baselines: SAUNet HATNet DGUNet+ OCTUF+ MADUN CPP-Net PnP-DRUNet PnP-DnCNN COAST CSformer
Builds on: ADMM half quadratic splitting SAUNet plug-and-play Restormer-style channel attention
Closest papers by meaning
- Time-Embedded Algorithm Unrolling for Computational MRI (NeurIPS 2025 · similarity 0.89)
- What's in a Prior? Learned Proximal Networks for Inverse Problems (ICLR 2024 · similarity 0.87)
- Unrolled denoising networks provably learn to perform optimal Bayesian inference (NeurIPS 2024 · similarity 0.87)
- Plug-and-Play image restoration with Stochastic deNOising REgularization (ICML 2024 · similarity 0.86)
- CPP-Net: Embracing Multi-Scale Feature Fusion into Deep Unfolding CP-PPA Network for Compressive Sensing (CVPR 2024 · similarity 0.86)
- PnP-Flow: Plug-and-Play Image Restoration with Flow Matching (ICLR 2025 · similarity 0.85)
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