投影梯度算法求解非线性反问题的αl_(1)-βl_(2)正则化

A Projected Gradient Method for αl_(1)-βl_(2) Regularization of Nonlinear Inverse Problems

研究非线性不适定算子方程A(x)=y的αl_(1)-βl_(2)稀疏正则化的求解问题.由于现有的ST-(αl_(1)-βl_(2))算法可以任意慢,将基于广义条件梯度方法的投影梯度算法推广至求解非线性反问题的非凸αl_(1)-βl_(2)稀疏正则化,并证明其稳定性.此外,通过Morozov偏差原则确定l_(1)-球约束半径R.

In this paper,the solution of αl_(1)-βl_(2) regularization of nonlinear ill-posed operator equation A(x)=y is investigated.The current ST-(αl_(1)-βl_(2)) algorithm can be arbitrarily slow,the projected gradient algorithm based on generalized conditional gradient method is used to solve the non-convex αl_(1)-βl_(2) regularization of nonliner inverse problems,and the proof of stability of the algorithm is given.In addition,a strategy to determine the radius R of l_(1)-ball constraint by Morozov’s discrepancy principle is proposed.