A Survey and an Extensive Evaluation of Popular Audio Declipping Methods

Pavel Záviška, Pavel Rajmic, Alexey Ozerov, and Lucas Rencker

This readme file describes the MATLAB toolbox accompanying the article from the title.
Published version of the article is available at https://ieeexplore.ieee.org/document/9281027.
Postprint is also available at https://arxiv.org/abs/2007.07663.

Along with the audio declipping survey, the toolbox also contains source codes to the follow-up article called Audio declipping performance enhancement via crossfading (see details below), and a new analysis Social Sparsity Declipper introduced in the conference paper called Analysis Social Sparsity Audio Declipper (see details below).

Requirements

The code has been developed in MATLAB version R2019b and has been tested in R2019b, R2020a, and R2022a. Several methods rely on the LTFAT toolbox (version 2.4.0 used) and Constrained OMP (C-OMP) algorithm relies on the CVX toolbox (version 2.2).

Quick Tutorial

To use this declipping toolbox, just download all the files, add them to the MATLAB path and make sure that the LTFAT toolbox and CVX toolbox are properly installed.

The toolbox is organized into several subfolders:

• "Evaluation_algorithms" contains the PEAQ method used in the paper to evaluate the objective quality of restoration. Unfortunately, PEMO-Q (also used in the paper) cannot be made part of the repository due to copyright issues.
• "Methods" contains all the algorithms used in the extensive evaluation except for the NMF-based method (not publicly available).
• "Numerical_results" contains ".mat" files with numerical results based on five different metrics (dSDR computed on the whole signal—dSDR_all, dSDR computed on the clipped samples only—dSDR_clipped, PEAQ, PEMO-Q, and Rnonlin). Suffix "RR" denotes replacing the reliable samples of the restored signals before evaluation. The specific values are arranged in a matrix, where rows represent individual audio excerpts, and columns represent input SDR values.
• "Sounds" contains wav-files used for testing and a mat file with the testing signals "Sound_database.mat"
• "Tools" contains auxiliary methods for clipping the signal and computing the SDR.

The toolbox is designed to be run from the root folder of the toolbox. Each method in the "Methods" folder contains a "main" file that runs the declipping experiment for the selected audio signal and a clipping threshold (defined by the input SDR). It is possible to select an audio file from the preset or you can use your audio file. Furthermore, it is possible to select the input SDR and other parameters corresponding to the used algorithm and signal representation.

One main file could run one or more algorithms. The algorithm is chosen with the algorithm variable. This setting applies to:

• main_l1_relaxation.m
  • in param.algorithm select 'DR' for the Douglas-Rachford algorithm (synthesis model) or 'CP' for the Chambolle-Pock algorithm (analysis model);
  • in param.reweighting select "1" for reweighting of the coefficients (Rl1CC algorithms);
  • in param.weighting select "1" for parabola weighting of the coefficients
• main_csl1.m
  • in param.algorithm select 'csl1' for the non-weighted variant, 'pcsl1' for the psychoacoustically weighted variant and 'pwcsl1' for the parabola-weighted variant;
• main_Social_Sparsity.m
  • in shrinkage select 'EW' for Empirical Wiener and 'PEW' for Persistent Empirical Wiener
• main_SPADE.m
  • in param.algorithm select 'aspade' for the analysis variant of SPADE and 'sspade_new' for the (proper) synthesis variant of SPADE

The other main files (with SQAM suffix) can be run to reproduce the results from the paper—it declipps all ten audio files with the seven input distortion levels used (70 combinations in total). Note that such computation can be time consuming.

Default parameter values are identical to the values used for the experiments in the paper. For different sounds the optimum parameters could differ.

Special Thanks

The authors would like to thank:

• Lucas Rencker for providing the implementation of the Dictionary Learning method and for running the computations of the Dictionary Learning and the Constrained OMP.
• Valentin Emiya for providing the implementation of the Constrained OMP and the Janssen method.
• Matthieu Kowalski for providing the implementation of the Social Sparsity Declipper.
• Ondřej Mokrý for running the computations of the Janssen method.

Audio Excerpts

If you only want to listen to the audio excerpts, you can visit the web page: https://rajmic.github.io/declipping2020/

How to cite this toolbox

Please cite the following paper:

P. Záviška, P. Rajmic, A. Ozerov and L. Rencker, “A Survey and an Extensive Evaluation of Popular Audio Declipping Methods,” IEEE Journal of Selected Topics in Signal Processing, vol. 15, no. 1, pp. 5–24, Jan. 2021, doi: 10.1109/JSTSP.2020.3042071.

License

The code of this toolbox is distributed under the terms of the GNU Public License version 3.

References

• A. Adler, V. Emiya, M. Jafari, M. Elad, R. Gribonval, and M. Plumbley, “A constrained matching pursuit approach to audio declipping,” in 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), May 2011, pp. 329–332.

• S. Kitić, N. Bertin, and R. Gribonval, “Sparsity and cosparsity for audio declipping: a flexible non-convex approach,” in 12th International Conference on Latent Variable Analysis and Signal Separation (LVA/ICA), Aug. 2015, pp. 243–250.

• P. Záviška, P. Rajmic, O. Mokrý, and Z. Průša, “A proper version of synthesis-based sparse audio declipper,” in 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), May 2019, pp. 591–595.

• P. Rajmic, P. Záviška, V. Veselý, and O. Mokrý, “A new generalized projection and its application to acceleration of audio declipping,” Axioms, vol. 8, no. 3, 2019.

• A. J. Weinstein and M. B. Wakin, “Recovering a clipped signal in sparseland,” Sampling Theory in Signal and Image Processing, vol. 12, no. 1, pp. 55–69, 2013.

• K. Siedenburg, M. Kowalski, and M. Dorfler, “Audio declipping with social sparsity,” in 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), May 2014, pp. 1577–1581.

• B. Defraene, N. Mansour, S. D. Hertogh, T. van Waterschoot, M. Diehl, and M. Moonen, “Declipping of audio signals using perceptual compressed sensing,” IEEE Transactions on Audio, Speech, and Language Processing, vol. 21, no. 12, pp. 2627–2637, 2013.

• P. Záviška, P. Rajmic, and J. Schimmel, “Psychoacoustically motivated audio declipping based on weighted l1 minimization,” in 2019 42nd International Conference on Telecommunications and Signal Processing (TSP), July 2019, pp. 338–342.

• L. Rencker, F. Bach, W. Wang, and M. D. Plumbley, “Consistent dictionary learning for signal declipping,” in 14th International Conference on Latent Variable Analysis and Signal Separation (LVA/ICA). July 2018, pp. 446–455.

• A. J. E. M. Janssen, R. N. J. Veldhuis, and L. B. Vries, “Adaptive interpolation of discrete-time signals that can be modeled as autoregressive processes,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 34, no. 2, pp. 317–330, 1986.

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Audio Declipping Performance Enhancement via Crossfading

Pavel Záviška, Pavel Rajmic, and Ondřej Mokrý

This article can be viewed as the follow-up to the Audio Declipping Survey, focused on enhancing the performance of the audio declipping methods that produce solutions inconsistent in the reliable part.
Published version of the article is available at https://www.sciencedirect.com/science/article/pii/S0165168421004023.
Preprint of the article is available at https://arxiv.org/abs/2104.03074.

Quick Tutorial

The source code is one m-file called "crossfaded_replace_reliable.m", which is stored in the "Replace_reliable" folder. Before running this function, make sure the folder is in MATLAB path.

In the first step, run an arbitrary declipping algorithm that produces solutions inconsistent in the reliable part of the signal, such as:

• Constrained Orthogonal Matching Pursuit (C-OMP),
• Social Sparsity with Empirical Wiener (SS EW),
• Social Sparsity with Persistent Empirical Wiener (SS PEW),
• Compressed Sensing method minimizing ℓ1-norm (CSL1),
• Perceptual Compressed Sensing method minimizing ℓ1-norm (PCSL1),
• Parabola-Weighted Compressed Sensing method minimizing ℓ1-norm (PWCSL1),
• Dictionary Learning approach (DL).

The second step consists of replacing the reliable samples using the above-mentioned function. The default settings are the ones used in the experiments. So, to reproduce the results from the letter, call

output = crossfaded_replace_reliable(x, xc, Mr)

where:

• x is output from the declipping algorithm, i.e., vector of the reconstructed signal,
• xc is a vector of the clipped signal,
• Mr is a logical vector of the reliable mask (has ones in the reliable positions).

It is also possible to directly specify the parameters of the method by calling

output = crossfaded_replace_reliable(x, xc, Mr, flag, w, transition_type, treat_short)

where:

• flag specifies the position of the crossfading transition:
  • 0 means the old traditional way of replacing all reliable samples (RR),
  • 1 means a transition in the clipped part,
  • 2 means a transition in the reliable part,
  • 3 means a transition in both parts,
• w determines the length of the crossfading transition in samples,
• transition_type affects the type of the crossfade,
  • 'linear' uses the linear crossfade,
  • 'soft' uses the soft crossfade modeled using squared sine function,
• treat_short specifies the way of treating the segments that are shorter than w:
  • 0 ignores the short segments,
  • 1 replaces the short segments using the traditional (RR) way without crossfading,
  • 2 uses the longest possible length of crossfade to fit the short segment.

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Analysis Social Sparsity Audio Declipper

Pavel Záviška and Pavel Rajmic

This conference paper introduces an analysis variant of the popular Social Sparsity Audio declipper using the Loris–Verhoeven optimization algorithm.
Published version of the paper is available at https://ieeexplore.ieee.org/document/9851269.
The postprint of the paper can be found at https://arxiv.org/abs/2205.10215.

Source m-files are appended to the existing directory structure and can be found in the "Methods/Social Sparsity" directory. The proposed algorithm is implemented in "main_Analysis_Social_Sparsity.m".

Apart from the proposed analysis variant of the algorithm itself, a newly added feature is also weighting of the time-frequency coefficients (similar to l1 relaxation algorithms), which is available for both the synthesis and analysis variants of the Social Sparsity algorithm. The weighting can be enabled by setting the weighting variable to true. The default option is the parabola weights, which quadratically grow with frequency and therefore penalize higher frequencies. These weights are computed in the function "comp_weights". Nonetheless, it is possible to use any type of weights.

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Pavel Záviška, Brno University of Technology, 2022