Parameter retrieval is a typical nonconvex optimization problem in a wide range of research and engineering fields. Classic methods tackle the parameter retrieval problem by feature extraction from the subspace or transform domain. In this paper, we proposed a network-based method to directly solve the nonconvex optimization problem on parameters estimation of complex exponential signals, with no requirement of labeled data. The proposed network has an architecture similar to the Autoencoder network but with the decoder sub-network replaced by a complex exponential signal generator. After training the network to fit the signal parameters to the acquired data, one could obtain the parameters, i.e., frequencies, decay rates, and intensities, and reconstruct the signal. By this work, we show that with a simple application of a lightweight neural network, nonconvex optimization problems like parameter retrieval can be solved efficiently, even without any intricately designed algorithms. We also discuss the robustness of the network-based method by repeated experiments and present the failure cases to indicate the limitations of this method.

中文翻译：

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非凸优化的神经网络方法及其在参数检索中的应用


参数检索是广泛研究和工程领域中典型的非凸优化问题。经典方法通过从子空间或变换域提取特征来解决参数检索问题。在本文中，我们提出了一种基于网络的方法来直接解决复杂指数信号参数估计的非凸优化问题，不需要标记数据。所提出的网络具有与自动编码器网络类似的架构，但解码器子网络被复杂指数信号发生器取代。在训练网络使信号参数与获取的数据相匹配后，可以获得频率、衰减率和强度等参数，并重建信号。通过这项工作，我们表明，通过轻量级神经网络的简单应用，即使没有任何复杂设计的算法，也可以有效地解决参数检索等非凸优化问题。我们还通过重复实验讨论了基于网络的方法的鲁棒性，并提出了失败案例以表明该方法的局限性。