Deep Atomic Norm Denoising Network for Jointly Range-Doppler Estimation With FRI Sampling

Finite rate of innovation (FRI) sampling is widely used in modern high-resolution range-Doppler (RD) detection systems to reduce the sampling rate. However, as the sampling rate decreases, the method becomes more noise-sensitive. This study proposes a deep atomic norm denoising network (DAND-Net) to denoise FRI samples of RD signals and estimate the noise levels (NLs). Based on the sparse common support property of the FRI samples, the denoising problem of the RD signals was modeled as an atomic norm soft thresholding problem, which jointly used multiple measurement vectors and could be unfolded into a model-driven deep network. The trainability and generalization ability of the network were improved by introducing piecewise linear functions and new trainable variables. By introducing an NL estimation operator, the NL could be better estimated during denoising, and the network training and convergence better supported. Additionally, the plug-and-play method could be used to complete denoising prior to many existing FRI methods. The simulation experiments showed that the proposed denoising network can achieve better denoising and NL estimation results with fewer iterations.