Development of a Solvability Map.
Development of a Solvability Map.
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DOI：
10.18103/mra.v10i11.3312
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发表时间：
2023
期刊：
影响因子：
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通讯作者：
Zeng, Gengsheng L
中科院分区：
文献类型：
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作者：
Zeng, Gengsheng L
有时，有必要确定是否有足够的测量用于图像重建任务，特别是当使用非标准扫描几何结构时。当成像系统可以被近似地建模为线性方程组时，系统矩阵的条件数指示整个系统是否可以作为整体稳定地求解。当系统整体不能稳定求解时，可通过奇异值分解（SVD）求出Moore-Penrose伪逆矩阵，从而得到广义解。然而，这些方法并不实用，因为它们需要计算机存储器来存储整个系统矩阵，而系统矩阵通常太大而无法存储。此外，我们不知道广义解是否足够好。本文提出了一种实用的图像可解性图，它可以为任何实际的图像重建算法。该图像可解性图使用大量计算机模拟的随机幻影测量每个位置的重建误差。换句话说，地图是通过蒙特卡罗方法生成的。
From time to time, it is necessary to determine whether there are sufficient measurements for the image reconstruction task especially when a non-standard scanning geometry is used. When the imaging system can be approximately modeled as a system of linear equations, the condition number of the system matrix indicates whether the entire system can be stably solved as a whole. When the system as a whole cannot be stably solved, the Moore-Penrose pseudo inverse matrix can be evaluated through the singular value decomposition (SVD) and then a generalized solution can be obtained. However, these methods are not practical because they require the computer memory to store the whole system matrix, which is often too large to store. Also, we do not know if the generalized solution is good enough for the application in mind. This paper proposes a practical image solvability map, which can be obtained for any practical image reconstruction algorithm. This image solvability map measures the reconstruction errors for each location using a large number of computer-simulated random phantoms. In other words, the map is generated by a Monte Carlo approach.