An upper bound is derived for a figure of merit that quantifies the error in reconstructed pixel or voxel values induced by the presence of null functions for any list-mode system. It is shown that this upper bound decreases as the region in attribute space occupied by the allowable attribute vectors expands. This upper bound allows quantification of the reduction in this error when this type of expansion is implemented. Of course, reconstruction error is also caused by system noise in the data, which has to be treated statistically, but we will not be addressing that problem here. This method is not restricted to pixelized or voxelized reconstructions and can in fact be applied to any region of interest. The upper bound for pixelized reconstructions is demonstrated on a list-mode 2D Radon transform example. The expansion in the attribute space is implemented by doubling the number of views. The results show how the pixel size and number of views both affect the upper bound on reconstruction error from null functions. This reconstruction error can be averaged over all pixels to give a single number or can be plotted as a function on the pixel grid. Both approaches are demonstrated for the example system. In conclusion, this method can be applied to any list-mode system for which the system operator is known and could be used in the design of the systems and reconstruction algorithms.

中文翻译：

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属性空间大小增加对列表模式成像系统零空间的影响

得出品质因数的上限，该品质因数量化了任何列表模式系统的空函数的存在所导致的重构像素或体素值中的误差。结果表明，该上限随着属性空间中被允许的属性向量占据的区域的扩大而减小。当实施这种类型的扩展时，该上限允许量化该误差的减小。当然，重建错误也是由数据中的系统噪声引起的，必须对它进行统计处理，但是在此我们将不解决该问题。该方法不限于像素化或体素化的重建，并且实际上可以应用于任何感兴趣的区域。在列表模式2D Radon变换示例中演示了像素化重建的上限。属性空间的扩展是通过将视图数量加倍来实现的。结果显示像素大小和视图数如何影响空函数导致的重构误差上限。可以将所有像素的重建误差取平均值，得到一个单一的数字，也可以将其作为函数绘制在像素网格上。两种方法都针对示例系统进行了演示。总之，该方法可以应用于系统操作员已知的任何列表模式系统，并且可以用于系统设计和重构算法中。可以将所有像素的重建误差取平均值，得到一个单一的数字，也可以将其作为函数绘制在像素网格上。两种方法都针对示例系统进行了演示。总之，该方法可以应用于系统操作员已知的任何列表模式系统，并且可以用于系统设计和重构算法中。可以将所有像素的重建误差取平均值，得到一个单一的数字，也可以将其作为函数绘制在像素网格上。两种方法都针对示例系统进行了演示。总之，该方法可以应用于系统操作员已知的任何列表模式系统，并且可以用于系统设计和重构算法中。