Computational auditory induction as a missing-data model-fitting problem with Bregman divergence

Roux, Jonathan Le; Kameoka, Hirokazu; Cheveigné, Alain de; Sagayama, Shigeki

doi:10.1016/j.specom.2010.08.009

Cited by 24 publications

(22 citation statements)

References 42 publications

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“…3 It is assumed that 1 As opposed to [3], earlier works on audio inpainting with NMF/NTF models [9,11] cannot optimally address arbitrary losses in time domain, since the missing data are formulated in time frequency domain. 2 This work would be readily extended to the multi-channel case.…”

Section: Signal Model and Problem Formulationmentioning

confidence: 99%

“…This approach, based on non-negative matrix factorization (NMF) performs as well or better than the state of the art group sparsity based methods such as [10]. It builds on the recent successes of NMF [7] and non-negative tensor factorization (NTF) in audio inpainting [9,11,3] 1 . Since, NMF/NTF framework is also very powerful in source separation [13,5,8], it lends itself to addressing the joint problem of audio inpainting and audio source separation.…”

Section: Introductionmentioning

confidence: 99%

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Joint Audio Inpainting and Source Separation

Bilen

Ozerov

Pérez

2015

Latent Variable Analysis and Signal Separation

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Abstract. Despite being two important problems in audio signal processing that are interconnected in practice, audio inpainting and audio source separation have not been considered jointly. It is not uncommon in practice to have the mixtures to be separated which also suffer from artifacts due to clipping or other losses. In present work, we consider this problem of source separation using partially observed mixtures. We introduce a flexible framework based on non-negative tensor factorisation (NTF) to attack this new task, and we apply it to source separation with clipped mixtures. It allows us to perform declipping and source separation either in turn or jointly. We investigate experimentally these two regimes and report large performance gains compared to source separation with clipping artefacts being ignored, which is the common approach in practice.

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Section: Signal Model and Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Joint Audio Inpainting and Source Separation

Bilen

Ozerov

Pérez

2015

Latent Variable Analysis and Signal Separation

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“…A natural strategy consists in performing a spectrogram inpainting stage, where the amplitude of the missing coefficients are estimated, followed by a phase inpainting stage, where the missing phases are estimated. While spectrogram inpainting has been addressed in several works [14,11,9], phase inpainting has not been addressed by advanced methods and thus remains a challenge. Indeed, phase reconstruction is known to be a difficult task generally posed as a non-convex problem.…”

Section: Introductionmentioning

confidence: 99%

Phase Reconstruction for Time-Frequency Inpainting

Kreme

Emiya

Chaux

2018

Latent Variable Analysis and Signal Separation

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Abstract. We address the problem of phase inpainting, i.e. the reconstruction of partially-missing phases in linear measurements. We thus aim at reconstructing missing phases of some complex coefficients assuming that the phases of the other coefficients as well as the modulus of all coefficients are known. The mathematical formulation of the inverse problem is first described and then, three methods are proposed: a first one based on the well known Griffin and Lim algorithm and two other ones based on positive semidefinite programming (SDP) optimization methods namely PhaseLift and PhaseCut, that are extended to the case of partial phase knowledge. The three derived algorithms are tested with measurements from a short-time Fourier transform (STFT) in two situations: the case where the missing data are distributed uniformly and indepedently at random and the case where they constitute holes with a given width. Results show that the knowledge of a subset of phases contributes to improve the signal reconstruction and to shorten the convergence of the optimization process.

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“…Such an extension of CNMF is worth being considered, as it opens the way to data-reconstruction settings with nonnegative low-rank constraints, which covers several relevant applications. One example concerns the field of image or audio inpainting [5,6,7,8], where CNMF may improve the current reconstruction techniques. In inpainting of audio spectrograms for example, setting up the dictionary to be a comprehensive collection of notes from a specific instrument may guide the factorization toward a realistic and meaningful decomposition, increasing the quality of the reconstruction of the missing data.…”

Section: Introductionmentioning

confidence: 99%

Convex nonnegative matrix factorization with missing data

Hamon

Emiya

Févotte

2016

2016 IEEE 26th International Workshop on Machine Learning for Signal Processing (MLSP)

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. (NMF) in which the components are a convex combination of atoms of a known dictionary. In this contribution, we propose to extend CNMF to the case where the data matrix and the dictionary have missing entries. After a formulation of the problem in this context of missing data, we propose a majorization-minimization algorithm for the solving of the optimization problem incurred. Experimental results with synthetic data and audio spectrograms highlight an improvement of the performance of reconstruction with respect to standard NMF. The performance gap is particularly significant when the task of reconstruction becomes arduous, e.g. when the ratio of missing data is high, the noise is steep, or the complexity of data is high.

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Computational auditory induction as a missing-data model-fitting problem with Bregman divergence

Cited by 24 publications

References 42 publications

Joint Audio Inpainting and Source Separation

Joint Audio Inpainting and Source Separation

Phase Reconstruction for Time-Frequency Inpainting

Convex nonnegative matrix factorization with missing data

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