Quadratic Neural Networks for Solving Inverse Problems

被引：0

作者：

Frischauf, Leon ^{[1
]}

Scherzer, Otmar ^{[1
,2
,3
]}

Shi, Cong ^{[1
,2
,4
]}

机构：

[1] Univ Vienna, Fac Math, Vienna, Austria

[2] Johann Radon Inst Computat & Appl Math RICAM, Linz, Austria

[3] Christian Doppler Lab Math Modeling & Simulat Next, Vienna, Austria

[4] Univ Vienna, Fac Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2024年 / 45卷 / 02期

基金：

奥地利科学基金会;

关键词：

Generalized neural network functions; inverse problems; MULTILAYER FEEDFORWARD NETWORKS; UNIVERSAL APPROXIMATION;

D O I：

10.1080/01630563.2024.2316580

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we investigate the solution of inverse problems with neural network ansatz functions with generalized decision functions. The relevant observation for this work is that such functions can approximate typical test cases, such as the Shepp-Logan phantom, better, than standard neural networks. Moreover, we show that the convergence analysis of numerical methods for solving inverse problems with shallow generalized neural network functions leads to more intuitive convergence conditions, than for deep affine linear neural networks.

引用

页码：112 / 135

页数：24

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