Γεώργιος Παπαγεωργίου

Georgios K. Papageorgiou, Mathini Sellathurai, Yonina C. Eldar

In this work, we consider direction-of-arrival (DoA) estimation in the presence of extreme noise using Deep Learning (DL). In particular, we introduce a Convolutional Neural Network (CNN) that is trained from mutli-channel data of the true array manifold matrix and is able to predict angular directions using the sample covariance estimate. We model the problem as a multi-label classification task and train a CNN in the low-SNR regime to predict DoAs across all SNRs. The proposed architecture demonstrates enhanced robustness in the presence of noise, and resilience to a small number of snapshots. Moreover, it is able to resolve angles within the grid resolution. Experimental results demonstrate significant performance gains in the low-SNR regime compared to state-of-the-art methods and without the requirement of any parameter tuning. We relax the assumption that the number of sources is known a priori and present a training method, where the CNN learns to infer the number of sources jointly with the DoAs. Simulation results demonstrate that the proposed CNN can accurately estimate off-grid angles in low SNR, while at the same time the number of sources is successfully inferred for a sufficient number of snapshots. Our robust solution can be applied in several fields, ranging from wireless array sensors to acoustic microphones or sonars.

George Papageorgiou, Pantelis Bouboulis, Sergios Theodoridis

We consider the task of robust non-linear regression in the presence of both inlier noise and outliers. Assuming that the unknown non-linear function belongs to a Reproducing Kernel Hilbert Space (RKHS), our goal is to estimate the set of the associated unknown parameters. Due to the presence of outliers, common techniques such as the Kernel Ridge Regression (KRR) or the Support Vector Regression (SVR) turn out to be inadequate. Instead, we employ sparse modeling arguments to explicitly model and estimate the outliers, adopting a greedy approach. The proposed robust scheme, i.e., Kernel Greedy Algorithm for Robust Denoising (KGARD), is inspired by the classical Orthogonal Matching Pursuit (OMP) algorithm. Specifically, the proposed method alternates between a KRR task and an OMP-like selection step. Theoretical results concerning the identification of the outliers are provided. Moreover, KGARD is compared against other cutting edge methods, where its performance is evaluated via a set of experiments with various types of noise. Finally, the proposed robust estimation framework is applied to the task of image denoising, and its enhanced performance in the presence of outliers is demonstrated.