Algebraic methods applied to the reconstruction of Sparse-view Computed Tomography (CT) can provide both a high image quality and a decrease in the dose received by patients, although with an increased reconstruction time since their computational costs are higher. In our work, we present a new algebraic implementation that obtains an exact solution to the system of linear equations that models the problem and based on single-precision floating-point arithmetic. By applying Out-Of-Core (OOC) techniques, the dimensions of the system can be increased regardless of the main memory size and as long as there is enough secondary storage (disk). These techniques have allowed to process images of 768 x 768$ pixels. A comparative study of our method on a GPU using both single-precision and double-precision arithmetic has been carried out. The goal is to assess the single-precision arithmetic implementation both in terms of time improvement and quality of the reconstructed images to determine if it is sufficient to consider it a viable option. Results using single-precision arithmetic approximately halves the reconstruction time of the double-precision implementation, whereas the obtained images retain all internal structures despite having higher noise levels.

翻译：应用于稀疏视图计算机断层扫描（CT）重建的代数方法能够在提高图像质量的同时降低患者所受辐射剂量，但其计算成本较高，导致重建时间相应增加。本研究提出一种基于单精度浮点运算的新型代数实现方法，该方案通过求解精确线性方程组来建模重建问题。借助外存计算技术，系统维度可突破主内存容量限制，仅需足够的二级存储（磁盘）空间即可处理大规模数据。该技术已成功实现768×768像素图像的并行处理。我们在GPU平台上对单精度与双精度算法进行了对比研究，旨在从时间效率与重建图像质量两方面评估单精度实现的可行性。实验结果表明：单精度算法重建时间较双精度方案缩短约50%，重建图像虽噪声水平较高，但完整保留了所有内部组织结构。