基于惩罚加权最小二乘法和引导全变差的量子压缩感知CT重建算法
Quantum Compressed Sensing CT Reconstruction Algorithm Based on Penalized Weighted Least Squares and Guided Total Variation
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中文总结 AI 辅助
研究针对现有基于QUBO的稀疏视图CT重建的局限，提出结合PWLS和GTV的量子压缩感知CT方法，经二进制编码形成统一QUBO模型，实验表明该方法重建质量最佳，为量子辅助稀疏视图CT重建提供了概念验证。
中文摘要 AI 辅助
目的。现有的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和解剖异质性。我们在QUBO框架内解决这两个限制。我们提出了一种结合惩罚加权最小二乘法（PWLS）和引导全变差（GTV）的量子压缩感知CT方法。PWLS通过光子计数可靠性对投影残差进行加权，而GTV使用由同步代数重建技术（SART）重建的先验图像的梯度来保留边缘并抑制均匀区域中的噪声。经过二进制编码后，这两个项形成一个统一的QUBO模型。实验使用了四个40×40的CT图像，在10视图扇形束几何结构下添加泊松噪声。比较包括传统重建方法、QUBO变体、梯度下降、模拟退火和D-Wave混合量子经典求解器。结果表明，PWLS-GTV在所有情况下都实现了最佳的重建质量。在代表性的胸部病例中，它达到了36.64 dB的峰值信噪比（PSNR），而最佳的传统基线SART为22.48 dB。GTV始终优于传统的全变差。模拟退火和D-Wave混合求解器产生了相似的重建结果，而梯度下降无效。重复运行混合求解器显示出稳定的结果。该框架在不改变其二次形式的情况下，将光子统计加权和结构引导正则化纳入基于QUBO的CT重建中，为量子辅助稀疏视图CT重建提供了概念验证。
英文摘要
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.
发表机构
- Peking University Health Science Center（北京大学医学部）
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