Deep Learning-Based 2-D Frequency Estimation of Multiple Sinusoidals

Frequency estimation of 2-D multicomponent sinusoidal signals is a fundamental issue in the statistical signal processing community that arises in various disciplines. In this article, we extend the DeepFreq model by modifying its network architecture and apply it to 2-D signals. We name the proposed framework 2-D ResFreq. Compared with the original DeepFreq framework, the 2-D convolutional implementation of the matched filtering module facilitates the transformation from time-domain signals to frequency-domain signals and reduces the number of network parameters. The additional upsampling layer and stacked residual blocks are designed to perform superresolution. Moreover, we introduce frequency amplitude information into the optimization function to improve the amplitude accuracy. After training, the signals in the test set are forward-mapped to 2-D accurate and high-resolution frequency representations. Frequency and amplitude estimation are achieved by measuring the locations and strengths of the spectral peaks. We conduct numerical experiments to demonstrate the superior performance of the proposed architecture in terms of its superresolution capability and estimation accuracy.