CIF: Small: Model-based sparse X-ray CT signal processing using polychromatic measurements

x射线CT测量系统在现代无损评价和医学诊断中具有重要意义。提高这些系统的重建精度和数据收集速度可能对这些广泛的领域产生重大影响。由于最近计算和理论的进步，现在可以设计迭代重建方法，将精确的非线性物理模型纳入明显欠采样测量的稀疏信号重建中。本研究旨在通过简化的非线性信号模型实现多色测量的精确x射线CT重建。研究人员开发了稀疏图像重建方法，用于盲场景下的多色CT测量，其中被测物体的材料和入射能谱未知。本研究建立在质量衰减参数化的基础上，建立了一个简单的多色x射线CT测量系统的信号模型。由于材料的质量衰减系数和测量系统的入射谱都是光子能量的函数，因此可以通过改变变量将光子能量从信号模型中去除，从而得到衰减后的信号强度的积分表达式具有拉普拉斯核形式。研究人员将入射谱表示为质量衰减的函数，并通过使用适当的基函数展开来估计它。一个主要的努力集中在开发类似的简单模型和相应的算法来重建由多种材料组成的物体。

X-ray CT measurement systems are important in modern nondestructive evaluation (NDE) and medical diagnostics. Improving reconstruction accuracy and speed of data collection in these systems could have a significant impact on these broad areas. Thanks to recent computational and theoretical advances, it is now possible to design iterative reconstruction methods that incorporate accurate nonlinear physical models into sparse signal reconstructions from significantly undersampled measurements. This research aims at achieving accurate X-ray CT reconstruction from polychromatic measurements via parsimonious nonlinear signal models.The investigators develop sparse image reconstruction methods for polychromatic CT measurements under the blind scenario where the material of the inspected object and the incident energy spectrum are unknown. This research builds on mass attenuation parametrization that leads to a simple signal model of a polychromatic X-ray CT measurement system. Since both the mass attenuation coefficient of a material and the incident spectrum of the measurement system are functions of the photon energy, photon energy can be removed from the signal model through a change of variables, leading to integral expressions of the attenuated signal strength having the Laplace kernel form. The investigators represent the incident spectrum as a function of mass attenuation and estimate it by using an appropriate basis-function expansion. A major effort focuses on developing similar simple models and corresponding algorithms for reconstructing objects consisting of multiple materials.