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Computational compressive imaging reconstruction with a simulated-annealing-based Ising solver
Ze Zheng, Xiaoyan Wu, Hang Xu, Jingzheng Huang, Tailong Xiao, Guihua Zeng
TL;DR
Compressive imaging poses an underdetermined reconstruction problem, while its computational demands can burden high-resolution and multidimensional recovery. This paper formulates the inverse problem as an Ising model and solves it with simulated annealing; the authors report higher reconstruction quality than mainstream algorithms in single-pixel and diffuser-camera demonstrations.
Problem
With fewer measurements than image pixels, the forward model is underdetermined and admits no unique exact solution.
Source: Methods · p. 2Method
The framework formulates data fidelity, sparsity, and smoothness terms as an Ising model and recovers the image from its minimum-energy spin configuration.
Source: Methods · pp. 2, 4Results
The simulated-annealing Ising framework achieves higher reconstruction quality than mainstream algorithms in single-pixel and lensless diffuser-camera simulations and experiments.
Source: Conclusion and Discussion · p. 8Takeaways & Limitations
The demonstrated framework applies to single-pixel imaging and lensless diffuser-camera reconstruction, with other imaging techniques and modalities identified as potential extensions.
Source: Conclusion and Discussion · p. 8The demonstrations use a double-precision simulated-annealing solver because available 8-bit Ising-machine encoding is insufficient for this problem.
Source: Methods · p. 5
Abstract
from arXiv · showhide
Computational compressive imaging, such as single-pixel imaging and lensless imaging, is a promising imaging technique, enabling the reconstruction of objects from under-sampled measurements through compressed sensing algorithms or deep learning methods. However, the demand for electronic computational resources grows rapidly when recovering high-resolution and multi-dimensional images and training neural networks with numerous parameters, which has become a bottleneck for the widespread adoption of this technique. Here, we propose a physics-driven reconstruction framework that formulates imaging inverse problems as Ising models and directly recovers target objects through the self-evolution of non-von Neumann Ising machines toward the ground state of the Hamiltonian. We employ a simulated-annealing-based Ising solver to demonstrate this proof-of-concept by reconstructing objects in both single-pixel imaging and a lensless diffuser camera at sampling rates ranging from 1% to 25%. By further incorporating a foreground-sparsity constraint and a smoothness constraint, the reconstruction quality of our method is comparable to or even better than that of mainstream algorithms. This approach has the potential to substantially reduce the electronic computational burden of inverse reconstruction, paving the way for real-time, low-power computational imaging.
Methods
The method converts an underdetermined optical measurement model into an Ising optimization problem, then reconstructs the image from the minimum-energy spin configuration. Adding foreground sparsity and smoothness yields better reported reconstruction quality across single-pixel and diffuser-camera demonstrations, although the solver uses double-precision simulated annealing.
Methods
- The method minimizes the data-fidelity loss derived from y = Ax, an underdetermined model with fewer measurements than image pixels, then reshapes the minimum-energy spin configuration into an image.For the diffuser camera, A is constructed from the pre-calibrated PSF; for single-pixel imaging, its rows represent illumination patterns.Source: Methods · pp. 2–3
- Foreground sparsity and smoothness augment the data-fidelity objective in Ising-SA-D, which produces higher reconstruction quality than data-fidelity-only Ising-SA at the same iteration.The smoothness term uses nearest-neighbor pixel connections, with four adjacent pixels treated as neighbors.Source: Methods · pp. 4, 6
- The demonstrations use double-precision simulated annealing because available 8-bit Ising-machine encoding makes the problem ill-conditioned and breaks equivalence to the original objective.The tested commercial 8-bit machine returns an all-white image; improving physical-machine encoding precision is proposed as a future path.Source: Methods · pp. 5–6
- At 2% sampling, Ising-SA-D reconstruction quality increases with iterations and exceeds the reported metrics of DGI, ADMM-TV, and GIDC at 100,000 iterations.The Ising Hamiltonian decreases while PSNR and SSIM increase during annealing.Source: Methods · pp. 5–6, Figure 2 · p. 5
- The experiments use 100,000 iterations; single-pixel reconstruction quality improves with sampling rate, and Ising-SA-D ranks above Ising-SA at each tested rate.Mainstream methods visually recover the targets but show higher-level background noise and lower SNR, PSNR, and SSIM than the proposed frameworks.Source: Figure 3 · p. 6, Methods · p. 7
- In diffuser-camera experiments at 8% and 16% sampling, Ising-SA and Ising-SA-D frameworks, each with 100,000 iterations, perform better than other methods at low sampling rates.Source: Figure 4 · p. 7, Methods · p. 8
Conclusion and Discussion
The framework formulates compressive imaging reconstruction as an Ising model and demonstrates higher reconstruction quality than mainstream algorithms in simulations and experiments. Its resource requirements remain a substantial constraint for physical implementation.
Conclusion and Discussion
- The simulated-annealing-based framework achieves higher reconstruction quality than mainstream algorithms in single-pixel imaging and lensless diffuser-camera simulations and experiments.The formulation includes data-fidelity, sparsity, and smoothness terms.Source: Conclusion and Discussion · p. 8
- The reconstruction objective combines data fidelity, sparsity, and smoothness terms derived from the optical forward model.Source: Conclusion and Discussion · p. 8
- Binary N×N images require O(N^2) spins and O(N^4) couplings, while grayscale images require O(aN^2) spins and O(a^2N^4) couplings.For 8-bit grayscale, a equals 256.Source: Conclusion and Discussion · p. 8
- The demonstrations reconstruct 64×64 binary images using 4,160 virtual spins, while large-scale fully connected Ising machines remain difficult to realize on physical platforms.Source: Conclusion and Discussion · p. 8
- Spatial photonic Ising machines have intrinsic full connectivity and are progressing toward larger size, complex couplings, and improved precision.Dedicated reconstruction frameworks for these machines may reduce hardware resource costs.Source: Conclusion and Discussion · p. 8
Appendix A: Reconstruction of other objects in experimental single-pixel imaging
The appendix presents single-pixel imaging results for the running-man and fish objects, comparing reconstruction methods across sampling rates.
Appendix A: Reconstruction of other objects in experimental single-pixel imaging
- Figure 5 compares PSNR, SSIM, and reconstructed images for the running-man object across five methods and sampling rates from 1% to 25%.Source: Figure 5 · p. 9
- Both figures show 64×64-pixel reconstructions, with a 0.5 cm scale bar.Source: Figure 5 · p. 9, Figure 6 · p. 9
- Figure 6 presents the corresponding PSNR, SSIM, and reconstructed-image comparisons for the fish object across the same five methods and sampling rates.Source: Figure 6 · p. 9