Being low-rank in the time-frequency plane

Valentin Emiya 1 Ronan Hamon 1 Caroline Chaux 2
1 QARMA - éQuipe d'AppRentissage de MArseille
LIS - Laboratoire d'Informatique et Systèmes
2 I2M - Institut de Mathématiques de Marseille
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.
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Communication dans un congrès
ICASSP - IEEE International Conference on Acoustics, Speech and Signal Processing, Apr 2018, Calgary, Canada. 2018, 〈https://2018.ieeeicassp.org/〉
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Soumis le : jeudi 16 novembre 2017 - 10:50:48
Dernière modification le : lundi 30 avril 2018 - 09:58:01
Document(s) archivé(s) le : samedi 17 février 2018 - 13:42:30

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UNIV-AMU | EC-MARSEILLE | I2M-2014- | I2M | LIS-LAB | UNIV-TLN

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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. 2018, 〈https://2018.ieeeicassp.org/〉. 〈hal-01636111〉

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