Being low-rank in the time-frequency plane

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.
Type de document :
Pré-publication, Document de travail
2017
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Contributeur : Valentin Emiya <>
Soumis le : jeudi 16 novembre 2017 - 10:50:48
Dernière modification le : lundi 29 janvier 2018 - 15:54:02
Document(s) archivé(s) le : samedi 17 février 2018 - 13:42:30

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Valentin Emiya, Ronan Hamon, Caroline Chaux. Being low-rank in the time-frequency plane. 2017. 〈hal-01636111〉

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