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：代数方法应用于稀疏视图计算机断层扫描（CT）重建，可在降低患者辐射剂量的同时获得高质量图像，但由于其计算成本较高，重建时间会相应增加。本研究提出一种新的代数实现方法，基于单精度浮点运算精确求解描述该问题的线性方程组。通过应用外核（OOC）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）空间即可扩展。该技术已实现768×768像素图像的完整处理。我们在GPU平台上对单精度与双精度运算版本进行了对比研究，旨在从重建时间优化和图像质量两个维度评估单精度运算实现的可行性。实验结果表明：单精度运算版本的重建时间约为双精度版本的一半，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。