A neural network method for nonconvex optimization and its application on parameter retrieval

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.