@article {625,
	title = {Passive sampling in reproducing kernel Hilbert spaces using leverage scores},
	journal = {Signal Processing},
	volume = {199},
	year = {2022},
	month = {May},
	abstract = {This paper deals with the selection of the training dataset in kernel-based methods for function reconstruction, with a focus on kernel ridge regression. A functional analysis is performed which, in the absence of noise, links the optimal sampling distribution to the one minimizing the difference between the kernel matrix and its low-rank Nystr{\"o}m approximation. From this standpoint, a statistical passive sampling approach is derived which uses the leverage scores of the columns of the kernel matrix to design a sampling distribution that minimizes an upper bound of the risk function. The proposed approach constitutes a passive method, able to select the optimal subset of training samples using only information provided by the input set and the kernel, but without needing to know the values of the function to be approximated. Furthermore, the proposed approach is backed up by numerical tests on real datasets.},
	doi = {https://doi.org/10.1016/j.sigpro.2022.108603},
	author = {Gimenez-Febrer, Pere and Pages-Zamora, Alba and Santamar{\'\i}a, Ignacio}
}
@article {601,
	title = {DOA Estimation via Shift-Invariant Matrix Completion},
	journal = {Signal Processing},
	volume = {183},
	year = {2021},
	abstract = {This paper presents a method to estimate the direction of arrival (DOA) of multiple sources received by a uniform linear array (ULA) with a reduced number of radio-frequency (RF) chains. The receiving array relies on antenna switching so that at every time instant only the signals received by a randomly selected subset of antennas are downconverted to baseband and sampled. Low-rank matrix completion (MC) techniques are then used to reconstruct the missing entries of the signal data matrix to keep the angular resolution of the original large-scale array. The proposed MC algorithm exploits not only the low- rank structure of the signal subspace, but also the shift-invariance property of ULAs, which results in a better estimation of the signal subspace. Further, the effect of MC on DOA estimation is discussed under the perturbation theory framework. The simulation results suggest that the proposed method provides accurate DOA estimates even in the small-sample regime with a significant reduction in the number of RF chains required for a given spatial resolution.},
	doi = {https://doi.org/10.1016/j.sigpro.2021.107993},
	author = {Garg, Vaibhav and Gimenez-Febrer, Pere and Pages-Zamora, Alba and Santamar{\'\i}a, Ignacio}
}
@conference {570,
	title = {Source Enumeration via Toeplitz Matrix Completion},
	booktitle = {Int. Conf. Acoustics, Speech and Signal Processing (ICASSP)},
	year = {2020},
	month = {May},
	pages = {6004-6008},
	address = {Barcelona, Spain},
	abstract = {This paper addresses the problem of source enumeration by an array of sensors in the presence of noise whose spatial covariance structure is a diagonal matrix with possibly different variances, referred to non-iid noise hereafter, when the sources are uncorrelated. The diagonal terms of the sample covariance matrix are removed and, after applying Toeplitz rectification as a denoising step, the signal covariance matrix is reconstructed by using a low-rank matrix completion method adapted to enforce the Toeplitz structure of the sought solution. The proposed source enumeration criterion is based on the Frobenius norm of the reconstructed signal covariance matrix obtained for increasing rank values. As illustrated by simulation examples, the proposed method performs robustly for both small and large-scale arrays with few snapshots, i.e. small-sample regime.},
	author = {Garg, Vaibhav and Gimenez-Febrer, Pere and Pages-Zamora, Alba and Santamar{\'\i}a, Ignacio}
}
