Filter factor analysis of scaled gradient methods for linear least squares

3rd International Workshop on New Computational Methods for Inverse Problems

物理学;计算机科学

Porta, Federica^1 ; Cornelio, Anastasia^1 ; Zanni, Luca^1 ; Prato, Marco^1

Department of Physics, Computer Science and Mathematics, University of Modena and Reggio Emilia, France^1

关键词: First-order algorithms;    Iteration numbers;    Iterative gradients;    Linear least squares;    Linear least squares problems;    Noise amplification;    Regularization approach;    Regularization parameters;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/464/1/012006/pdf
DOI  :  10.1088/1742-6596/464/1/012006

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

A typical way to compute a meaningful solution of a linear least squares problem involves the introduction of a filter factors array, whose aim is to avoid noise amplification due to the presence of small singular values. Beyond the classical direct regularization approaches, iterative gradient methods can be thought as filtering methods, due to their typical capability to recover the desired components of the true solution at the first iterations. For an iterative method, regularization is achieved by stopping the procedure before the noise introduces artifacts, making the iteration number playing the role of the regularization parameter. In this paper we want to investigate the filtering and regularizing effects of some first-order algorithms, showing in particular which benefits can be gained in recovering the filters of the true solution by means of a suitable scaling matrix.