[论文解读] Mixed one-bit compressive sensing with applications to overexposure correction for CT reconstruction

Xiaolin Huang, Yan Xia+5 more|arXiv (Cornell University)|Jan 3, 2017

Sparse and Compressive Sensing Techniques参考文献 31被引用 3

一句话总结

本文提出混合一比特压缩感知（M1bit-CS）以通过结合常规测量与饱和投影测量，校正C臂CT中的过曝伪影。基于ADMM的优化与迭代饱和检测，M1bit-CS即使在严重饱和情况下也能实现接近理想重建的精度，显著减少了条纹伪影与帽状伪影，优于现有方法。

ABSTRACT

When a measurement falls outside the quantization or measurable range, it becomes saturated and cannot be used in classical reconstruction methods. For example, in C-arm angiography systems, which provide projection radiography, fluoroscopy, digital subtraction angiography, and are widely used for medical diagnoses and interventions, the limited dynamic range of C-arm flat detectors leads to overexposure in some projections during an acquisition, such as imaging relatively thin body parts (e.g., the knee). Aiming at overexposure correction for computed tomography (CT) reconstruction, we in this paper propose a mixed one-bit compressive sensing (M1bit-CS) to acquire information from both regular and saturated measurements. This method is inspired by the recent progress on one-bit compressive sensing, which deals with only sign observations. Its successful applications imply that information carried by saturated measurements is useful to improve recovery quality. For the proposed M1bit-CS model, alternating direction methods of multipliers is developed and an iterative saturation detection scheme is established. Then we evaluate M1bit-CS on one-dimensional signal recovery tasks. In some experiments, the performance of the proposed algorithms on mixed measurements is almost the same as recovery on unsaturated ones with the same amount of measurements. Finally, we apply the proposed method to overexposure correction for CT reconstruction on a phantom and a simulated clinical image. The results are promising, as the typical streaking artifacts and capping artifacts introduced by saturated projection data are effectively reduced, yielding significant error reduction compared with existing algorithms based on extrapolation.

研究动机与目标

• 为解决因探测器动态范围有限而引起的C臂CT过曝问题，特别是在膝关节等薄体部结构中。
• 在部分投影因过曝而饱和的情况下，恢复高质量的CT图像。
• 开发一种有效利用饱和测量信息的方法，而这类信息在经典重建中通常被丢弃或处理不当。
• 通过引入一比特压缩感知原理，提升重建精度，超越现有外推与迭代检测方法。

提出的方法

• 提出一种混合一比特压缩感知（M1bit-CS）模型，将常规与饱和测量统一纳入恢复框架。
• 采用交替方向乘子法（ADMM）求解M1bit-CS中的非凸优化问题。
• 设计一种迭代饱和检测（ISD）方案，从数据中估计饱和指示矩阵Ψ，实现对过曝投影的准确识别。
• 整合关于组织结构的先验知识，以改善饱和检测与重建的初始估计。
• 将M1bit-CS模型应用于仿真与临床CT数据，以滤波反投影（FBP）与SART作为基线重建方法。
• 对饱和测量采用基于符号的观测模型，将其视为一比特数据，以保留有用的结构信息。

实验结果

研究问题

• RQ1 传统上被丢弃或处理不当的饱和CT投影，是否仍能为图像重建提供有用信息？
• RQ2 一比特压缩感知原理如何扩展以处理包含常规与饱和观测的混合测量？
• RQ3 迭代饱和检测方法是否能在无真实饱和模式先验知识的情况下，可靠识别投影数据中的过曝区域？
• RQ4 与采用外推或检测方案的经典FBP与SART相比，M1bit-CS在重建质量上提升程度如何？
• RQ5 M1bit-CS对饱和检测误差的鲁棒性如何？其性能与理想饱和指示矩阵的差距有多大？

主要发现

• 在κ=0.5p_max的膝关节体素模型中，M1bit-CSR-ISD的均方根误差（RMSE）为8.547 HU，显著低于FBP（182.4 HU）与SART-ISD（54.91 HU）。
• 在κ=0.6p_max的头部体素模型中，M1bit-CSR-ISD的RMSE为11.62 HU，优于FBP-WCE（35.34 HU）与SART-ISD（31.97 HU）。
• 在严重饱和条件下（κ=0.4p_max），M1bit-CSR-ISD的RMSE为14.81 HU，而SART-ISD与FBP-WCE无法保持清晰的外轮廓。
• M1bit-CSR-ISD与使用理想饱和矩阵的M1bit-CSR之间的差距较小（14.81 HU vs. 12.39 HU），表明对检测误差具有鲁棒性。
• 迭代饱和检测（ISD）方法正确识别了大部分饱和区域，误报与漏检极少，如图14所示。
• 所提方法在体素与临床数据中均有效减少了条纹伪影与帽状伪影，实现了视觉与定量上均更优的重建效果。