论文标题
正则线性反问题的多项式预处理
Polynomial Preconditioners for Regularized Linear Inverse Problems
论文作者
论文摘要
这项工作旨在加快用于解决正则线性逆问题的近端梯度方法的收敛性。这是通过设计基于多项式的预处理来实现的，该预处理针对源自线性运算符的正常运算符的特征值光谱。预处理器不假定线性函数上的任何明确结构，因此可以部署在各种关注的应用程序中。在三种不同的磁共振成像应用程序上验证了预处理的功效，在该应用中，它可以看到更快的迭代收敛，同时实现相似的重建质量。
This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal operator derived from the linear operator. The preconditioner does not assume any explicit structure on the linear function and thus can be deployed in diverse applications of interest. The efficacy of the preconditioner is validated on three different Magnetic Resonance Imaging applications, where it is seen to achieve faster iterative convergence while achieving similar reconstruction quality.
