NsigNet: A Neural Network Design for Detecting the Number of Signals Under Sparse Observations

Many estimation and reconstruction algorithms in signal processing fields can be improved themselves if the number of signals is known. However, this assumption of preknowledge is challenging in real environments. Additionally, it is often necessary to obtain the information of physical parameters of the signal through a short data acquisition time, i.e., a small number of samples, in systems requiring the low latency. Accordingly, an algorithm to effectively detect the number of signals through a small number of samples can be of great help to various estimation and reconstruction algorithms as the preprocessor for them. In this article, we introduce a new algorithm which detects the number of signals with the efficiently designed neural network (NN), referred to as NsigNet. The proposed method is based on optimizing the NN by inputting the singular values of the reshaped informative matrix from the sampled signal and outputting the one-hot encoding vectors indicating the number of signals. Simulation results show that NsigNet outperforms the conventional schemes in the various environments. Notably, the proposed scheme requires extremely small number of training data set and network size. Finally, we provide two applications, i.e., (i) sparse signal recovery with compressive sensing and (ii) signal denoising with the iterative
$K$
-truncated singular value decomposition (SVD), to validate the benefit of NsigNet in the practical on-/off-grid problems, respectively.