论文标题
通过过滤的对角框架分解来正规化反问题
Regularization of Inverse Problems by Filtered Diagonal Frame Decomposition
论文作者
论文摘要
反问题的特征是它们在数据扰动方面的不稳定。为了稳定反转过程，必须开发和应用正则化方法。在这项工作中，我们介绍和分析了过滤的对角线框架分解的概念，该分解将标准过滤的奇异值分解扩展到框架情况。作为广义单数系统的框架可以更好地适应给定的潜在解决方案。在本文中，我们表明过滤后的对角线框架分解产生了收敛的正则化方法。此外，我们在源类型条件下得出收敛速率，并在假设被考虑的框架为riesz-basis的假设下证明了秩序最优性。
The characteristic feature of inverse problems is their instability with respect to data perturbations. In order to stabilize the inversion process, regularization methods have to be developed and applied. In this work we introduce and analyze the concept of filtered diagonal frame decomposition which extends the standard filtered singular value decomposition to the frame case. Frames as generalized singular system allows to better adapt to a given class of potential solutions. In this paper, we show that filtered diagonal frame decomposition yield a convergent regularization method. Moreover, we derive convergence rates under source type conditions and prove order optimality under the assumption that the considered frame is a Riesz-basis.
