On Krylov methods for large-scale CBCT reconstruction
On Krylov methods for large-scale CBCT reconstruction
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DOI：
10.1088/1361-6560/acd616
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发表时间：
2023-08-07
影响因子：
3.5
通讯作者：
Schonlieb，Carola-Bibiane
中科院分区：
文献类型：
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作者：
Landman，Malena Sabate;Biguri，Ander;Schonlieb，Carola-Bibiane
Krylov子空间方法是解线性方程组的一类强大的迭代求解器，由于其固有的正则化性质，常用于反问题。此外，这些方法自然适合于解决大规模问题，因为它们只需要与系统矩阵(及其伴随矩阵)的矩阵向量乘积来计算近似解，并且它们具有非常快的收敛速度。即使这类方法已经在数值线性代数界得到了广泛的研究和研究，但它在应用医学物理和应用工程中的应用仍然非常有限。例如，在现实的大规模计算机断层扫描(CT)问题中，更具体地说，在锥束CT(CBCT)中。这项工作试图通过为应用于三维CT问题的最相关的Krylov子空间方法提供一个通用框架来打破这一空白，包括最著名的用于非方系统(CGLS，LSQR，LSMR)的Krylov求解器，可能与Tikhonov正则化相结合，以及结合全变分正则化的方法。这是在一个开放源码框架内提供的：基于层析迭代GPU的重建工具箱，其想法是促进所提出算法的结果的可访问性和重复性。最后，给出了模拟和实际三维CT应用(医用CBCT和μ-CT数据集)的数值结果，展示和比较了本文提出的不同的Krylov子空间方法，以及它们对不同类型问题的适用性。
Krylov subspace methods are a powerful family of iterative solvers for linear systems of equations, which are commonly used for inverse problems due to their intrinsic regularization properties. Moreover, these methods are naturally suited to solve large-scale problems, as they only require matrix-vector products with the system matrix (and its adjoint) to compute approximate solutions, and they display a very fast convergence. Even if this class of methods has been widely researched and studied in the numerical linear algebra community, its use in applied medical physics and applied engineering is still very limited. eg in realistic large-scale computed tomography (CT) problems, and more specifically in cone beam CT (CBCT). This work attempts to breach this gap by providing a general framework for the most relevant Krylov subspace methods applied to 3D CT problems, including the most well-known Krylov solvers for non-square systems (CGLS, LSQR, LSMR), possibly in combination with Tikhonov regularization, and methods that incorporate total variation regularization. This is provided within an open source framework: the tomographic iterative GPU-based reconstruction toolbox, with the idea of promoting accessibility and reproducibility of the results for the algorithms presented. Finally, numerical results in synthetic and real-world 3D CT applications (medical CBCT and μ-CT datasets) are provided to showcase and compare the different Krylov subspace methods presented in the paper, as well as their suitability for different kinds of problems.