Abstract We propose a new approach to constructing globally strictly convex objective functional in a 1-D inverse medium scattering problem using multi-frequency backscattering data. The global convexity of the proposed objective functional is proved. We also prove the global convergence of the gradient projection algorithm and derive an error estimate. Numerical examples are presented to illustrate the performance of the proposed algorithm.

中文翻译：

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使用新的多频全局严格凸目标函数解决一维逆介质散射问题

摘要 我们提出了一种使用多频反向散射数据在一维逆介质散射问题中构建全局严格凸目标函数的新方法。证明了所提出的目标函数的全局凸性。我们还证明了梯度投影算法的全局收敛性并得出了一个误差估计。给出了数值例子来说明所提出算法的性能。