基于Elastic-net正则化的神经网络方法求解反问题  

Neural Network Method Based on Elastic-net Regularization for Solving Inverse Problem

作　　者：李龙[1] 丁亮[1] Li Long;Ding Liang(Northeast Forestry University)

机构地区：[1]东北林业大学

出　　处：《哈尔滨师范大学自然科学学报》2024年第1期1-8,共8页Natural Science Journal of Harbin Normal University

基　　金：黑龙江省教育科学“十四五”规划2022年度重点课题(GJB1422738)。

摘　　要：神经网络已经成为求解反问题的热点方法之一,引入elastic-net正则项作为神经网络中损失函数的惩罚项防止求解过程的过度拟合,并通过交叉训练实现基于elastic-net正则项的神经网络的算法.通过压缩感知和图像去模糊2个数值实验,验证elastic-net正则项防止过度拟合的可行性和有效性.此外,当变换矩阵条件数较大时,在较低的训练轮次下可以达到较好的训练效果.At present,neural network has become one of the hot methods to solve inverse problems.In this paper,the elastic-net regularization is introduced as the penalty term of the loss function in the neural network to prevent the overfitting of the problem,and the algorithm of the neural network based on elasticnet regularization is realized by cross training.Through two numerical experiments of compressive sensing and image deblurring,the feasibility and effectiveness of the elastic-net regularization to prevent overftting are verified.Furthermore,when the condition number of the transformation matrix is large,better training results can be achieved under lower training rounds.

关 键 词：反问题 神经网络 elastic-net正则化 压缩感知 图像去模糊 

分 类 号：O29[理学—应用数学]