Quantum Compressed Sensing CT Reconstruction Algorithm Based on Penalized Weighted Least Squares and Guided Total Variation

2026-07-12

AI Summary

This work addresses the limitations of existing QUBO-based sparse-view CT reconstruction methods, which neglect photon-counting statistics and anatomical heterogeneity. The authors propose a quantum-inspired compressed sensing approach that integrates penalized weighted least squares (PWLS) with guided total variation (GTV), leveraging gradient information from an SART-generated prior image to steer regularization. Crucially, the entire model is reformulated into a quadratic unconstrained binary optimization (QUBO) framework while preserving its quadratic structure, thereby incorporating both photon-statistics-based weighting and structural guidance for the first time within a QUBO formulation. In experiments reconstructing 40×40 chest CT images from only 10 projection views, the method achieves a PSNR of 36.64 dB—substantially outperforming conventional SART (22.48 dB) and other QUBO variants—demonstrating its efficacy and robustness for high-quality reconstruction in quantum-computing-oriented imaging.

Abstract

Objective. Existing quadratic unconstrained binary optimization (QUBO)-based sparse-view computed tomography (CT) reconstruction neglects photon-counting statistics and anatomical heterogeneity. We address both limitations within the QUBO framework.Approach. We propose a quantum compressed-sensing CT method combining penalized weighted least squares (PWLS) and guided total variation (GTV). PWLS weights projection residuals by photon-count reliability, whereas GTV uses gradients from a prior image reconstructed by the simultaneous algebraic reconstruction technique (SART) to preserve edges and suppress noise in homogeneous regions. After binary encoding, both terms form a unified QUBO model. Experiments used four 40 times 40 CT images under a 10-view fan-beam geometry with Poisson noise. Comparisons included conventional reconstruction methods, QUBO variants, gradient descent, simulated annealing, and a D-Wave hybrid quantum-classical solver.Main results. PWLS-GTV achieved the best reconstruction quality across all cases. In the representative chest case, it reached a peak signal-to-noise ratio (PSNR) of 36.64 dB, compared with 22.48 dB for SART, the best conventional baseline. GTV consistently outperformed conventional total variation. Simulated annealing and the D-Wave hybrid solver produced similar reconstructions, whereas gradient descent was ineffective. Repeated hybrid-solver runs showed stable performance.Significance. The framework incorporates photon-statistical weighting and structure-guided regularization into QUBO-based CT reconstruction without changing its quadratic form, providing a proof of concept for quantum-assisted sparse-view CT reconstruction.

Problem

• QUBO
• sparse-view CT reconstruction
• photon-counting statistics
• anatomical heterogeneity
• compressed sensing

Innovation

• Quantum Compressed Sensing
• QUBO
• Penalized Weighted Least Squares
• Guided Total Variation
• Sparse-view CT Reconstruction