通过稀疏矩阵近似加速基于优化的计算机断层扫描
Accelerating optimization-based computed tomography via sparse matrix approximations
AI总结：
本文提出利用稀疏矩阵乘法减少计算机断层扫描重建中计算瓶颈，提升迭代算法效率并保持重建质量。
摘要：
变分法在计算机断层扫描重建中的应用具有显著缺点，即需要重复计算正向Radon变换及其伴随或近似反变换，这相对昂贵。本文探讨了两种方法，通过用稀疏矩阵乘法近似变换计算来减少这种计算瓶颈。第一种方法适用于通用迭代优化算法，第二种适用于误差遗忘算法如分裂Bregman算法。我们证明这些近似显著减少了求解重建问题所需迭代算法的计算时间，同时仍能提供良好的重建结果。
英文摘要：
Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are relatively expensive. We look at two methods for reducing the effect of this resulting computational bottleneck via approximating the transform evaluation with sparse matrix multiplications. The first method is applicable for general iterative optimization algorithms. The second is applicable in error-forgetting algorithms such as split Bregman. We demonstrate these approximations significantly reduce the needed computational time needed for the iterative algorithms needed to solve the reconstruction problem while still providing good reconstructions.
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