Exploiting Sparse Recovery Algorithms for Semi-Supervised Training of Deep Neural Networks for Direction-of-Arrival Estimation

This paper proposes a semi-supervised training approach for a direction-of-arrival (DoA) estimation based on a convolutional neural network (CNN). We apply a sparse recovery algorithm called optMGD-L1-SVD on the training dataset consisting of only unlabeled observed data to obtain binarized pseudo-spectra regarded as the CNN training targets (labels). The estimated DoAs are obtained at test time by performing peak picking on the CNN outputs. optMGD-L1-SVD has been shown to perform well with a few sensors under low signal-to-noise ratio (SNR) conditions (up to -6 dB) by optimally reweighting the pseudo-spectra of L1-SVD based on the application of group delay function on the pseudo-spectra of MUSIC. Since its hyperparameters are noise-sensitive, we assume that the SNR levels of the training dataset are known such that we can use the optimal ones. We also consider multi-condition training using data of multiple SNR levels to improve the robustness towards different noisy environments. We evaluated the proposed network, named optMGD-L1-SVD-CNN and MGD-L1-SVD-CNN, in terms of the average root-mean-square error and the resolution probability under low SNR conditions (up to -20 dB). We demonstrated that it performed well with a few sensors and snapshots, including at SNR levels unseen in the training data.