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De la faiblesse de rang en temps-fréquence

Abstract : The low-rank assumption for spectrogram has been widely used recently for the analysis of audio signals. In this paper, we are interested in time-frequency representations, and more particularly in the rank of the matrix of coefficients obtained after a Short-Time Fourier Transform (STFT). We show that the rank depends on the adopted convention to compute the STFT, and that its behaviour is similar to the one of spectrograms. We apply this result to an audio restoration problem, where missing data are present in the time-frequency plane. The missing complex coefficients are retrieved using a proximal algorithm minimizing the nuclear norm of the STFT matrix, accounting for the low-rank assumption.
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Submitted on : Tuesday, August 8, 2017 - 5:48:59 PM
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Ronan Hamon, Caroline Chaux, Valentin Emiya. De la faiblesse de rang en temps-fréquence. GRETSI, Sep 2017, Juan-Les-Pins, France. ⟨hal-01573204⟩

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