量子压缩感知提升低剂量CT重建质量，兼顾光子统计与解剖结构。
Quantum Compressed Sensing CT Reconstruction Algorithm Based on Penalized Weighted Least Squares and Guided Total Variation
- 融合加权最小二乘与引导总变差，提升重建精度。
- 在10视角下峰值信噪比达36.64 dB，显著优于传统方法。
- 首次实现量子优化框架内融合物理模型与结构先验，适合医学影像研究者。
现有基于二次无约束二进制优化（QUBO）的稀疏视图计算机断层扫描（CT）重建忽略了光子计数统计特性与解剖异质性。本文在QUBO框架内同时解决这两项局限。提出一种结合罚加权最小二乘（PWLS）与引导总变差（GTV）的量子压缩感知CT重建方法：PWLS根据光子可靠性加权投影残差，GTV则利用SART重建的先验图像梯度来保持边缘、抑制均匀区域噪声。经二值编码后，两项构成统一的QUBO模型。实验采用4幅40×40的CT图像，在10视角扇形束几何与泊松噪声条件下进行对比。评估方法包括传统重建算法、多种QUBO变体、梯度下降、模拟退火及D-Wave混合量子-经典求解器。结果表明：PWLS-GTV在所有情况下表现最佳；以代表性胸部案例为例，其峰值信噪比（PSNR）达36.64 dB，远超最优传统基准SART的22.48 dB；GTV始终优于传统总变差。模拟退火与D-Wave混合求解器性能相近，而梯度下降效果不佳；重复运行验证了混合求解器稳定性。该框架在不改变QUBO二次形式的前提下，将光子统计加权与结构引导正则化引入量子辅助稀疏视图重建，为量子计算在医学成像中的应用提供了概念验证。
原文摘要 · Abstract (English)
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.
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