ECM - École Centrale de Marseille : UMR7373 (Pôle de l'étoile - Technopole de Château-Gombert - 38 rue Frédéric Joliot-Curie - 13013 Marseille - France)
Abstract : When solving inverse problems and using optimization methods with matrix variables in signal processing and machine learning, it is customary to assume some low-rank prior on the targeted solution. Nonnegative matrix factorization of spectrograms is a case in point in audio signal processing. However, this low-rank prior is not straightforwardly related to complex matrices obtained from a short-time Fourier – or discrete Gabor – transform (STFT), which is generally defined from and studied based on a modulation operator and a translation operator applied to a so-called window. This paper is a first study of the low-rankness property of time-frequency matrices. We characterize the set of signals with a rank-r (complex) STFT matrix in the case of a unit hop size and frequency step with few assumptions on the transform parameters. We discuss the scope of this result and its implications on low-rank approximations of STFT matrices.
https://hal-amu.archives-ouvertes.fr/hal-01636111
Contributor : Valentin Emiya
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Submitted on : Thursday, November 16, 2017 - 10:50:48 AM
Last modification on : Thursday, January 23, 2020 - 6:22:12 PM
Long-term archiving on: Saturday, February 17, 2018 - 1:42:30 PM
Valentin Emiya, Ronan Hamon, Caroline Chaux. Being low-rank in the time-frequency plane. ICASSP - IEEE International Conference on Acoustics, Speech and Signal Processing, Apr 2018, Calgary, Canada. ⟨hal-01636111⟩
