Authors: Jijun Lu, Yifan Chen, Libang Chen, Yiqiang Zhou, Ye Zheng, Mingliang Chen, Zhe Sun, Xuelong Li
Organizations: Institute of Artificial Intelligence (TeleAI), China Telecom, China · School of Integrated Circuits, Shanghai Jiao Tong University, Shanghai, China · College of Future Information Technology, Fudan University, Shanghai, China · Aerospace Laser Technology and System Department, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, China · School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Xi’an, China · Fujian Ocean Innovation Center, Xiamen, China
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.
Figures & tables
Figure 1: Overview of the proposed method: (a) Core reconstruction workflow of the SISTA-Net algorithm. (b) Experimental setup for single-pixel imaging.
Figure 2: Architecture of the Data Fidelity Module. (a) The architecture of Res2MM-Net. (b) The structure of MamCNN Block. (c) The structure of Res2Mam Multi-Scale Block. (d) The structure of Window Mamba Block. (e) The structure of the Vision State Space Block.
Figure 3: Architecture of the Proximal Mapping Module. (a) The structure of the Sparsity Encoder. (b) The structure of the Sparsity Decoder. (c) The structure of the ResBlock.
Figure 4: Reconstruction results on binary images. The markers (A)–(I) denote DGI, ISTA-Net++, TransCS, Restormer, URNet, GILM, UNet, GIDC, and Ours in order.
Method
Bird
Grass
Raven
Tower
PSNR
SSIM
PSNR-HF
PSNR
SSIM
PSNR-HF
PSNR
SSIM
PSNR-HF
PSNR
SSIM
PSNR-HF
DGI
7.67
0.0288
18.40
6.91
0.0442
15.79
7.30
0.0224
13.00
7.38
0.0213
20.37
ISTA-Net++
6.23
0.0497
19.52
7.19
0.0875
16.27
7.08
0.0390
13.40
7.16
0.0273
22.15
TransCS
6.47
0.0400
19.36
6.79
0.0542
15.93
7.02
0.0212
13.19
9.26
0.0257
22.18
Restormer
14.18
0.1375
16.21
12.40
0.2414
14.47
10.45
0.0589
11.68
17.76
0.0823
19.58
URNet
16.44
0.1297
21.36
13.10
0.1775
17.07
12.48
0.0653
13.05
14.14
0.0512
18.59
Table 1: Quantitative comparison for simulated binary and grayscale reconstructions.
Figure 5: Reconstruction results on complex grayscale natural images.
Figure 6: Detail reconstruction results. (a) Reconstructed images and their locally enlarged regions. (b) Vertical grayscale intensity profiles at the mark.
Figure 7: Convergence and stability analysis. (a) PSNR curves of different models under five random seeds. (b) Intermediate SISTA-Net reconstruction results at selected epochs under random seed 0.
Figure 8: Reconstruction results over different sampling ratios. The markers (A)–(I) denote DGI, ISTA-Net++, TransCS, Restormer, URNet, GILM, UNet, GIDC, and Ours in order.
Figure 9: Evolution of sparse latent feature maps.
SR(N)
Epoch
Mean
E1%
E3%
E5%
2.93% (3k)
200
0.0393
0.7821
0.8717
0.9123
400
0.0051
0.9586
0.9812
0.9891
800
0.0014
0.9521
0.9796
0.9884
5.86% (6k)
200
0.0250
0.8648
0.9249
0.9501
400
0.0033
0.9697
0.9869
0.9925
800
0.0010
0.9652
0.9860
0.9922
Table 2: Latent feature metrics.
Figure 10: Reconstruction results under Gaussian, Poisson, and mixed noise. Noise strength increases from left to right.
Gaussian noise
Level
60 dB
55 dB
50 dB
45 dB
40 dB
Threshold
0.0345
0.0353
0.0391
0.0412
0.0472
Poisson noise
Level
1×106
5×105
1×105
5×104
1×104
Threshold
0.0368
0.0389
0.0385
0.0403
0.0465
Mixed noise
Table 3: Learnable thresholds under different noise levels.
Figure 11: Experimental setup for underwater SPI.
Figure 12: Reconstruction and ablation results.(I) Reconstruction results. (II) Network module ablation. (III) Loss function ablation.
Electronic Materials Research Laboratory, Key Laboratory of the Ministry of Education and International Center for Dielectric Research, School of Electronic Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, China · Micius Laboratory, Henan Academy of Sciences, Zhengzhou 450052, China · Department of Pharmacy, the First Affiliated Hospital of Xi’an Jiaotong University, Xi’an 710061, China +1
Electrical and Computer Engineering Department, University of California, Los Angeles, CA, 90095, USA · Bioengineering Department, University of California, Los Angeles, CA, 90095, USA · California NanoSystems Institute (CNSI), University of California, Los Angeles, CA, 90095, USA
College of Science, Northwest Agriculture & Forestry University, Yangling 712100, China · Key Laboratory of Photoelectronic Imaging Technology and System, School of Optics and Photonics, Beijing Institute of Technology, Beijing, China · State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China