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Singular value decomposition for photon-processing nuclear imaging systems and applications for reconstruction and computing null functions

机译：光子处理核成像系统的奇异值分解及其在重建和计算空函数中的应用

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摘要

Recent advances in technology are enabling a new class of nuclear imaging systems consisting of detectors that use real-time maximum-likelihood (ML) methods to estimate the interaction position, deposited energy, and other attributes of each photon-interaction event and store these attributes in a list format. This class of systems, which we refer to as photon-processing (PP) nuclear imaging systems, can be described by a fundamentally different mathematical imaging operator that allows processing of the continuous-valued photon attributes on a per-photon basis. Unlike conventional photon-counting (PC) systems that bin the data into images, PP systems do not have any binning-related information loss. Mathematically, while PC systems have an infinite-dimensional null space due to dimensionality considerations, PP systems do not necessarily suffer from this issue. Therefore, PP systems have the potential to provide improved performance in comparison to PC systems. To study these advantages, we propose a framework to perform the singular-value decomposition (SVD) of the PP imaging operator. We use this framework to perform the SVD of operators that describe a general two-dimensional (2D) planar linear shift-invariant (LSIV) PP system and a hypothetical continuously rotating 2D single-photon emission computed tomography (SPECT) PP system. We then discuss two applications of the SVD framework. The first application is to decompose the object being imaged by the PP imaging system into measurement and null components. We compare these components to the measurement and null components obtained with PC systems. In the process, we also present a procedure to compute the null functions for a PC system. The second application is designing analytical reconstruction algorithms for PP systems. The proposed analytical approach exploits the fact that PP systems acquire data in a continuous domain to estimate a continuous object function. The approach is parallelizable and implemented for graphics processing units (GPUs). Further, this approach leverages another important advantage of PP systems, namely the possibility to perform photon-by-photon real-time reconstruction. We demonstrate the application of the approach to perform reconstruction in a simulated 2D SPECT system. The results help to validate and demonstrate the utility of the proposed method and show that PP systems can help overcome the aliasing artifacts that are otherwise intrinsically present in PC systems.
机译：技术上的最新进展使一类新型的核成像系统成为可能，该系统由使用实时最大似然（ML）方法估算每个光子相互作用事件的相互作用位置，沉积能量和其他属性并存储这些属性的探测器组成以列表格式。这类系统，我们称为光子处理（PP）核成像系统，可以用根本不同的数学成像运算符来描述，该运算符允许在每个光子的基础上处理连续值的光子属性。与将数据分装到图像中的常规光子计数（PC）系统不同，PP系统没有任何与分装有关的信息丢失。从数学上讲，尽管PC系统由于尺寸方面的考虑而具有无限维的零空间，但PP系统不一定会遇到此问题。因此，与PC系统相比，PP系统具有提供改进性能的潜力。为了研究这些优点，我们提出了执行PP成像算子的奇异值分解（SVD）的框架。我们使用此框架来执行算子的SVD，该算子描述了一般的二维（2D）平面线性平移（LSIV）PP系统和假设的连续旋转2D单光子发射计算机断层扫描（SPECT）PP系统。然后，我们讨论SVD框架的两个应用程序。第一项应用是将PP成像系统成像的物体分解为测量分量和零分量。我们将这些组件与PC系统获得的测量和零组件进行比较。在此过程中，我们还介绍了计算PC系统空函数的过程。第二个应用程序是设计PP系统的解析重建算法。所提出的分析方法利用了PP系统在连续域中获取数据以估计连续对象功能这一事实。该方法可并行化，并针对图形处理单元（GPU）实施。此外，该方法利用了PP系统的另一个重要优势，即可以进行逐个光子的实时重建。我们演示了该方法在模拟2D SPECT系统中执行重建的应用。结果有助于验证和证明所提出方法的实用性，并表明PP系统可以帮助克服PC系统中固有存在的混叠伪像。

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