InpaintingNMF

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This is the accompanying repository for the article Algorithms for audio inpainting based on probabilistic nonnegative matrix factorization authored by Ondřej Mokrý, Paul Magron, Thomas Oberlin and Cédric Févotte, published in Elsevier Signal Processing.

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# InpaintingNMF

This is the accompanying repository for the article *Algorithms for audio inpainting based on probabilistic nonnegative matrix factorization* authored by Ondřej Mokrý, Paul Magron, Thomas Oberlin and Cédric Févotte, published in Elsevier Signal Processing.

> Audio inpainting, i.e., the task of restoring missing or occluded audio signal samples, usually relies on sparse representations or autoregressive modeling. In this paper, we propose to structure the spectrogram with nonnegative matrix factorization (NMF) in a probabilistic framework. First, we treat the missing samples as latent variables, and derive two expectation–maximization algorithms for estimating the parameters of the model, depending on whether we formulate the problem in the time- or time-frequency domain. Then, we treat the missing samples as parameters, and we address this novel problem by deriving an alternating minimization scheme. We assess the potential of these algorithms for the task of restoring short- to middle-length gaps in music signals. Experiments reveal great convergence properties of the proposed methods, as well as competitive performance when compared to state-of-the-art audio inpainting techniques.

The preprint is available at [arXiv](https://arxiv.org/abs/2206.13768) and [HAL](https://hal.inria.fr/hal-03708613), the paper is OA and published at [ScienceDirect](https://www.sciencedirect.com/science/article/pii/S0165168422004443).

## Contents

The repository includes the MATLAB source codes needed to reproduce the research, as well as some supplementary data and figures.

- **figures** – Exported plots as generated by the codes in **results**.
- **references** – Implementation of several candidates for the state of the art in audio inpainting, with the help of [InpaintingRevisited](https://github.com/ondrejmokry/InpaintingRevisited) and [Dictionary learning for sparse audio inpainting](https://www.oeaw.ac.at/isf/forschung/fachbereiche-teams/mathematik/dictionary-learning-for-sparse-audio-inpainting).
- **results** – Data and scripts to plot them.
- **signals** – Signals used for testing.
- **utils** – All the functions needed to run the main files.

## Psychoacoustically motivated evaluation

Note that the psychoacoustically motivated metrics (PEMO-Q, PEAQ) are not computed inside the main testing file `inpainting_comparison.m`. This evaluation could be performed by
1. uncommenting the lines related to signal saving in `inpainting_comparison.m` and running the whole experiment,
2. running the file `inpainting_comparison_add_odgs.m`.

The PEAQ package is included in the **utils** subfolder (acquired from [TSP Lab of McGill University](http://www-mmsp.ece.mcgill.ca/Documents/Software/)). However, the PEMO-Q software is no longer publicly available, thus it is not shared as part of this repository. For that reason, and because the processing is very time- and spacedemanding, the provided .mat files in the **results** subfolder include all the data precomputed.

## Further dependencies

- The functions related to short-time Fourier transform rely on the [Large Time-Frequency Analysis Toolbox](http://ltfat.org/).
- The dictionary learning method used as reference uses the [CVX toolbox](http://cvxr.com/cvx/).
- These codes were written in Matlab R2021a. Some functions may not be available in older versions of Matlab, e.g. `tiledlayout`, used commonly for plotting, was introduced in version R2019b.

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