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ADMM for ND Line Spectral Estimation using Grid-Free Compressive Sensing from Multiple Measurements with Applications to DOA Estimation

: Semper, Sebastian; Römer, Florian


Sanei, Saeid (General Chair) ; Institute of Electrical and Electronics Engineers -IEEE-; IEEE Signal Processing Society:
ICASSP 2019, IEEE International Conference on Acoustics, Speech and Signal Processing. Proceedings : May 12-17, 2019, Brighton
Piscataway, NJ: IEEE, 2019
ISBN: 978-1-4799-8131-1
ISBN: 978-1-4799-8132-8
International Conference on Acoustics, Speech, and Signal Processing (ICASSP) <44, 2019, Brighton>
Deutsche Forschungsgemeinschaft DFG
Fraunhofer-Gesellschaft FhG
025-601128; ATTRACT
Fraunhofer IZFP ()
doa estimation; Compressed Sensing (CS); Line Spectral Estimation; Sparse Signal Recovery (SSR); optimization

This paper is concerned with estimating unknown multidimensional frequencies from linear compressive measurements. This is accomplished by employing the recently proposed atomic norm minimization framework to recover these frequencies under a sparsity prior without imposing any grid restriction on these frequencies. To this end, we give a rigorous derivation of an iterative scheme called alternating direction of multipliers method, which is able to incorporate multiple compressive snapshots from a multi-dimensional superposition of complex harmonics. The key result here is how to formulate the objective function minimized by this scheme and its partial derivatives, which become hard to manage if the dimensionality of the frequencies is larger than 1. Moreover we demonstrate the performance of this approach in case of 3D line spectral estimation and 2D DOA estimation with a synthetic antenna array.