A novel meshless reconstruction algorithm for digital tomosynthesis (DT) is presented and assessed against experimental data. The algorithm does not require a three-dimensional grid or mesh allocation and performs a slice-by-slice reconstruction where each slice position can be chosen at runtime. The methodology is based on the filtered backprojection algorithm adapted to DT. However, in the traditional approach the backprojection comes first and the filtering follows. Because the backprojection requires ray tracing, in our case it is replaced with an equivalent image mapping procedure. The idea to swap the filtering and backprojection had been introduced earlier for computerized tomography (CT). Here we use this idea but develop it differently. Contrary to CT imaging, where the source and detector are rotated, in DT the subject and the flat panel detector are fixed in space. This imaging geometry allows reconstruction in planes parallel to the flat panel detector, which results in a significant simplification of the filter of backprojection algorithm. Moreover, the algorithm is not memory demanding and can be used with very large datasets. Two versions of the meshless algorithm are presented. One of them is based on convolution type filtering, while another uses filtering in the Fourier domain. Both versions are assessed and compared against the cone beam algorithm.

中文翻译：

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用于数字断层合成的无网格重建技术。

提出了一种新颖的无网格重建算法，用于数字层析合成（DT）并针对实验数据进行了评估。该算法不需要三维网格或网格分配，而是执行逐个切片的重构，其中可以在运行时选择每个切片的位置。该方法基于适用于DT的滤波反投影算法。但是，在传统方法中，反投影首先出现，然后进行滤波。因为反投影需要光线追踪，所以在我们的案例中，它被等效的图像映射过程替代。交换滤波和反投影的想法已在较早的计算机断层扫描（CT）中引入。在这里，我们使用了这个想法，但是发展了不同的想法。与CT成像相反，在该成像中，源和探测器旋转，在DT中，对象和平板检测器固定在空间中。这种成像几何结构允许在平行于平板检测器的平面中进行重构，从而显着简化了反投影算法的滤波器。此外，该算法对内存的要求不高，可以用于非常大的数据集。提出了两种版本的无网格算法。其中一种基于卷积类型过滤，而另一种则使用傅立叶域中的过滤。两种版本都经过评估，并与锥束算法进行了比较。该算法对内存的要求不高，可以用于非常大的数据集。提出了两种版本的无网格算法。其中一种基于卷积类型过滤，而另一种则使用傅立叶域中的过滤。两种版本都经过评估，并与锥束算法进行了比较。该算法对内存的要求不高，可以用于非常大的数据集。提出了两种版本的无网格算法。其中一种基于卷积类型过滤，而另一种则使用傅立叶域中的过滤。两种版本都经过评估，并与锥束算法进行了比较。