平行束几何中低剂量计算机断层扫描正则化重建方法的稳定性和鲁棒性分析
Stability and Robustness Analysis of Regularized Reconstruction Methods for Low-Dose Computed Tomography in Parallel-Beam Geometry
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中文总结 AI 辅助
研究低剂量计算机断层扫描正则化重建方法，基于Radon变换开发模拟管道，在多种噪声模型和采集几何下分析FBP、Tikhonov正则化和TV最小化的稳定性与鲁棒性，发现TV在多方面表现最佳，稳定性因子S能补充传统指标。
中文摘要 AI 辅助
低剂量计算机断层扫描（LDCT）减少了辐射暴露，但由于噪声和数据稀疏增加了重建问题的不适定性。虽然像Tikhonov和总变分（TV）这样的正则化方法提高了图像质量，但其性能严重依赖于噪声特性、采样条件和参数选择。本研究在二维平行束CT框架内对滤波反投影（FBP）、Tikhonov正则化和TV最小化进行了系统的稳定性和鲁棒性分析。基于Radon变换开发了统一的模拟管道，并使用修改后的Shepp-Logan体模和临床胸部图像进行评估。在涉及高斯、泊松和混合噪声模型的多种退化场景下，跨基线（180个投影）和稀疏视图（60个投影）采集几何结构研究重建行为。通过基于SSIM的详尽网格搜索针对每种场景优化正则化参数。通过RMSE、PSNR和SSIM评估质量，通过经验稳定性因子S量化鲁棒性，该因子测量从测量空间到图像空间的扰动放大。结果表明，FBP对噪声和欠采样高度敏感。与FBP相比，Tikhonov正则化提高了结构保真度，但对扰动仍比TV更敏感。相反，TV在噪声抑制、边缘保留、准确性和数值稳定性之间提供了最佳折衷。这些发现突出了LDCT中的稳定性-分辨率权衡，并表明所提出的稳定性因子S为传统指标提供了有价值的补充信息。
英文摘要
Low-dose computed tomography (LDCT) reduces radiation exposure but increases the ill-posedness of the reconstruction problem due to noise and sparse data. While regularized methods like Tikhonov and Total Variation (TV) improve image quality, their performance depends heavily on noise characteristics, sampling conditions, and parameter selection. This study presents a systematic stability and robustness analysis of Filtered Back Projection (FBP), Tikhonov regularization, and TV minimization within a 2D parallel-beam CT framework. A unified simulation pipeline based on the Radon transform is developed and evaluated using both the modified Shepp-Logan phantom and a clinical thorax image. Reconstruction behavior is investigated under multiple degradation scenarios involving Gaussian, Poisson, and mixed noise models, across baseline (180 projections) and sparse-view (60 projections) acquisition geometries. To ensure a fair comparison, regularization parameters are optimized for each scenario through an exhaustive SSIM-based grid-search. Quality is assessed via RMSE, PSNR, and SSIM, while robustness is quantified through an empirical Stability Factor S measuring perturbation amplification from measurement to image space. The results show that FBP is highly sensitive to noise and undersampling. Tikhonov regularization improves structural fidelity compared with FBP but remains more sensitive to perturbation than TV. Conversely, TV provides the best compromise between noise suppression, edge preservation, accuracy, and numerical stability. These findings highlight the stability-resolution trade-off in LDCT and demonstrate that the proposed Stability Factor S offers valuable complementary information to conventional metrics.
