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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<title>Audio Declipping</title>
<!--
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<meta name="description" content="Web page accompanying the article: A Survey and an Extensive Evaluation of Popular Audio Declipping Methods, containing extra figures and
listenable audio excerpts of the declipping algorithms.">
<meta name="keywords" content="Audio Clipping, Saturation, Declipping, Model, Sparsity, Learning, Optimization, Evaluation, Survey.">
<meta name="author" content="Pavel Záviška">
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<!-- <h3 class="wow fadeInUp" data-wow-delay="0.4s">Being an artist</h3> -->
<!--<h1 class="wow fadeInUp" data-wow-delay="0.2s">Audio Declipping</h1>-->
<!--<h3 class="wow fadeInUp" data-wow-delay="0.2s">A accompanying website for journal articles:</h3>-->
<h1 class="wow fadeInUp main-title" data-wow-delay="0.1s">Audio Declipping</h1>
<h1 class="wow fadeInUp article-titles" data-wow-delay="0.5s">A Survey and an Extensive Evaluation of Popular Audio Declipping Methods</h1>
<h4 class="wow fadeInUp" data-wow-delay="0.9s">
<a href="https://orcid.org/0000-0003-2221-2058">Pavel Záviška</a>,
<a href="https://orcid.org/0000-0002-8381-4442">Pavel Rajmic</a>,
<a href="https://orcid.org/0000-0002-7602-4610">Alexey Ozerov</a>,
<a href="https://orcid.org/0000-0002-9332-6602">Lucas Rencker</a>
</h4>
<!--<h4 class="wow fadeInUp" data-wow-delay="0.2s">and</h4>-->
<h1 class="wow fadeInUp article-titles" data-wow-delay="0.5s">Audio Declipping Performance Enhancement via Crossfading</h1>
<h4 class="wow fadeInUp" data-wow-delay="0.9s">
<a href="https://orcid.org/0000-0003-2221-2058">Pavel Záviška</a>,
<a href="https://orcid.org/0000-0002-8381-4442">Pavel Rajmic</a>,
<a href="https://orcid.org/0000-0003-1806-5809">Ondřej Mokrý</a>
</h4>
<h1 class="wow fadeInUp article-titles" data-wow-delay="0.5s">Audio Declipping with (Weighted) Analysis Social Sparsity</h1>
<h4 class="wow fadeInUp" data-wow-delay="0.9s">
<a href="https://orcid.org/0000-0003-2221-2058">Pavel Záviška</a>,
<a href="https://orcid.org/0000-0002-8381-4442">Pavel Rajmic</a>
</h4>
<div class="buttons">
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<h2>About</h2>
</div>
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<p>
This is an website accompanying three articles about Audio Declipping (see the abstracts below).
On this website you can find supplementary material such as a detailed description of the audio dataset used,
additional plots with results for each individual audio excerpt, a link to the repository with MATLAB source codes,
and last but not least, you can listen to the restored audio excerpts.
</p>
</div>
<div class="wow fadeInUp section-subtitle" data-wow-delay="0.2s">
<h3>A Survey and an Extensive Evaluation of Popular Audio Declipping Methods</h3>
</div>
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<p>
<b>Abstract:</b>
Dynamic range limitations in signal processing often lead to clipping, or saturation, in signals.
Audio declipping is the task of estimating the original audio signal given its clipped measurements and has attracted a lot of interest in recent years.
Audio declipping algorithms often make assumptions about the underlying signal, such as sparsity or low-rankness, as well as the measurement system.
In this paper, we provide an extensive review of audio declipping algorithms proposed in the literature.
For each algorithm, we present the assumptions being made about the audio signal, the modeling domain, as well as the optimization algorithm.
Furthermore, we provide an extensive numerical evaluation of popular declipping algorithms, on real audio data.
We evaluate each algorithm in terms of the Signal-to-Distortion Ratio, as well as using perceptual metrics of sound quality.
The article is accompanied with the repository containing the evaluated methods.
</p>
<p>
<b>Full-text:</b>
<a href="https://ieeexplore.ieee.org/document/9281027">IEEE Xplore</a>,
<a href="https://arxiv.org/abs/2007.07663">arXiv postprint</a>.
<br>
<b>Citations:</b>
<a href="bib/A_survey_and_an_extensive_evaluation_of_popular_audio_declipping_methods.txt" download="A_survey_and_an_extensive_evaluation_of_popular_audio_declipping_methods.txt">Plain Text</a>,
<a href="bib/A_survey_and_an_extensive_evaluation_of_popular_audio_declipping_methods.bib" download="A_survey_and_an_extensive_evaluation_of_popular_audio_declipping_methods.bib">BibTeX</a>.
</p>
</div>
<div class="wow fadeInUp section-subtitle" data-wow-delay="0.2s">
<h3>Audio declipping performance enhancement via crossfading</h3>
</div>
<div class="wow fadeIn" data-wow-delay="0.4s">
<p>
<b>Abstract:</b>
Some audio declipping methods produce waveforms that do not fully respect the physical process of clipping,
which is why we refer to them as inconsistent.
This letter reports what effect on perception it has if the solution by inconsistent methods is forced consistent by postprocessing.
We first propose a simple sample replacement method, then we identify its main weaknesses and propose an improved variant.
The experiments show that the vast majority of inconsistent declipping methods significantly benefit from the proposed approach in terms of objective perceptual metrics.
In particular, we show that the SS PEW method based on social sparsity combined with the proposed method performs comparable to top methods from the consistent class,
but at a computational cost of one order of magnitude lower.
</p>
<p>
<b>Full-text:</b>
<a href="https://www.sciencedirect.com/science/article/pii/S0165168421004023">ScienceDirect</a>,
<a href="https://arxiv.org/abs/2104.03074">arXiv preprint</a>.
<br>
<b>Citations:</b>
<a href="bib/Audio_declipping_performance_enhancement_via_crossfading.txt" download="Audio_declipping_performance_enhancement_via_crossfading.txt">Plain Text</a>,
<a href="bib/Audio_declipping_performance_enhancement_via_crossfading.bib" download="Audio_declipping_performance_enhancement_via_crossfading.bib">BibTeX</a>.
</p>
</div>
<div class="wow fadeInUp section-subtitle" data-wow-delay="0.2s">
<h3>Audio Declipping with (Weighted) Analysis Social Sparsity</h3>
</div>
<div class="wow fadeIn" data-wow-delay="0.4s">
<p>
<b>Abstract:</b>
We develop the analysis (cosparse) variant of the popular audio declipping algorithm of Siedenburg et al. (2014).
Furthermore, we extend both the old and the new variants by the possibility of weighting the time-frequency coefficients.
We examine the audio reconstruction performance of several combinations of weights and shrinkage operators.
The weights are shown to improve the reconstruction quality in some cases;
however, the best scores achieved by the non-weighted methods are not surpassed with the help of weights.
Yet, the analysis Empirical Wiener (EW) shrinkage was able to reach the quality of a computationally more expensive competitor, the Persistent Empirical Wiener (PEW).
Moreover, the proposed analysis variant incorporating PEW slightly outperforms the synthesis counterpart in terms of an auditorily motivated metric.
</p>
<p>
<b>Full-text:</b>
<a href="https://ieeexplore.ieee.org/document/9851269">IEEE Xplore</a>,
<a href="https://arxiv.org/abs/2205.10215">arXiv postprint</a>.
<br>
<b>Citations:</b>
<a href="bib/Audio_declipping_with_weighted_analysis_social_sparsity.txt" download="Audio_declipping_with_weighted_analysis_social_sparsity.txt">Plain Text</a>,
<a href="bib/Audio_declipping_with_weighted_analysis_social_sparsity.bib" download="Audio_declipping_with_weighted_analysis_social_sparsity.bib">BibTeX</a>.
</p>
</div>
</div>
</div>
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</section>
<!-- REPRODUCIBLE RESEARCH SECTION -->
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<h2>Reproducible Research</h2>
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<p>
Following the idea of reproducible research, we make all the implementations freely available at the <a
href="https://github.com/rajmic/declipping2020_codes">GitHub repository</a>.
<br>
Please note that LTFAT toolbox (version>=2.4.0, available <a href="https://ltfat.github.io">here</a>) must be installed and loaded
in order to run the scripts and reproduce the results.
</p>
</div>
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</section>
<!-- TABLE OF ALGORITHMS SECTION -->
<section id="abstract" class="parallax-section">
<div class="container">
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<h2>Algorithms</h2>
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<p>
The following table contains abbreviations and full names of the algorithms used in the evaluation.
<br>
Algorithms inconsistent in the reliable part of the clipped signal are marked with an asterisk *.
<br>
Note that the analysis variant of Social Sparsity declipper (ASS) was introduced later in the above-mentioned conference paper and thus it is not part of the Declipping Survey nor the Crossfading article.
</p>
<p>
<table style="width:100%">
<tr>
<th>Abbreviation</th>
<th>Full name</th>
</tr>
<tr>
<td>C-OMP*</td>
<td>Constrained Orthogonal Matching Pursuit</td>
</tr>
<tr>
<td>A-SPADE</td>
<td>Analysis SParse Audio DEclipper</td>
</tr>
<tr>
<td>S-SPADE</td>
<td>Synthesis SParse Audio DEclipper</td>
</tr>
<tr>
<td>ℓ<sub>1</sub> CP</td>
<td>ℓ<sub>1</sub>-minimization using Cambolle–Pock</td>
</tr>
<tr>
<td>ℓ<sub>1</sub> DR</td>
<td>ℓ<sub>1</sub>-minimization using Douglas–Rachford</td>
</tr>
<tr>
<td>Rℓ<sub>1</sub>CC CP</td>
<td>Reweighted ℓ<sub>1</sub>-minimization with Clipping Constraints using Chambolle–Pock (analysis)</td>
</tr>
<tr>
<td>Rℓ<sub>1</sub>CC DR</td>
<td>Reweighted ℓ<sub>1</sub>-minimization with Clipping Constraints using Douglas–Rachford (synthesis)</td>
</tr>
<tr>
<td>SS EW*</td>
<td>Social Sparsity with Empirical Wiener</td>
</tr>
<tr>
<td>SS PEW*</td>
<td>Social Sparsity with Persistent Empirical Wiener</td>
</tr>
<tr>
<td>CSL1*</td>
<td>Compressed Sensing method minimizing ℓ<sub>1</sub>-norm</td>
</tr>
<tr>
<td>PCSL1*</td>
<td>Perceptual Compressed Sensing method minimizing ℓ<sub>1</sub>-norm</td>
</tr>
<tr>
<td>PWCSL1*</td>
<td>Parabola-Weighted Compressed Sensing method minimizing ℓ<sub>1</sub>-norm</td>
</tr>
<tr>
<td>PWℓ<sub>1</sub> CP</td>
<td>Parabola-Weighted ℓ<sub>1</sub>-minimization using Chambolle–Pock (analysis)</td>
</tr>
<tr>
<td>PWℓ<sub>1</sub> DR</td>
<td>Parabola-Weighted ℓ<sub>1</sub>-minimization using Douglas–Rachford (synthesis)</td>
</tr>
<tr>
<td>DL*</td>
<td>Dictionary Learning approach</td>
</tr>
<tr>
<td>NMF</td>
<td>Nonnegative Matrix Factorization</td>
</tr>
<tr>
<td>Janssen</td>
<td>Janssen method for inpainting</td>
</tr>
<tr>
<td>ASS EW*</td>
<td>Analysis Social Sparsity with Empirical Wiener</td>
</tr>
<tr>
<td>ASS PEW*</td>
<td>Analysis Social Sparsity with Persistent Empirical Wiener</td>
</tr>
</table>
</p>
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</section>
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<h2>Audio Excerpts</h2>
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<p> The audio database used for the evaluation consists of
10 musical excerpts in mono, sampled at 44.1 kHz, with an
approximate length of 7 seconds. They were extracted from the
EBU SQAM database. The excerpts were thoroughly selected
to cover a wide range of audio signal characteristics. Since
a significant number of methods is based on signal sparsity, the
selection took care about including different levels of sparsity
in the signals (w.r.t. the Gabor transform).
</p>
</div>
</div>
<div class="col-md-12 col-sm-12" style="z-index:1">
<div class="wow fadeInUp col-md-2 col-md-offset-1 col-xs-6" data-wow-delay="0.4s">
<!-- WORK THUMB -->
<div class="work-thumb">
<a href="images/sounds/a08_violin.png" class="image-popup">
<img src="images/sounds/a08_violin.png" class="img-responsive" alt="a08_violin">
</a>
</div>
<div class="work-caption">
<h5> 01. violin </h5>
</div>
</div>
<div class="wow fadeInUp col-md-2 col-md-offset-1 col-xs-6" data-wow-delay="0.4s">
<!-- WORK THUMB -->
<div class="work-thumb">
<a href="images/sounds/a16_clarinet.png" class="image-popup">
<img src="images/sounds/a16_clarinet.png" class="img-responsive" alt="a16_clarinet">
</a>
</div>
<div class="work-caption">
<h5> 02. clarinet </h5>
</div>
</div>
<div class="wow fadeInUp col-md-2 col-md-offset-1 col-xs-6" data-wow-delay="0.4s">
<!-- WORK THUMB -->
<div class="work-thumb">
<a href="images/sounds/a18_bassoon.png" class="image-popup">
<img src="images/sounds/a18_bassoon.png" class="img-responsive" alt="a18_bassoon">
</a>
</div>
<div class="work-caption">
<h5> 03. bassoon </h5>
</div>
</div>
<div class="wow fadeInUp col-md-2 col-md-offset-1 col-xs-6" data-wow-delay="0.4s">
<!-- WORK THUMB -->
<div class="work-thumb">
<a href="images/sounds/a25_harp.png" class="image-popup">
<img src="images/sounds/a25_harp.png" class="img-responsive" alt="a25_harp">
</a>
</div>
<div class="work-caption">
<h5> 04. harp </h5>
</div>
</div>
<div class="wow fadeInUp col-md-2 col-md-offset-1 col-xs-6" data-wow-delay="0.4s">
<!-- WORK THUMB -->
<div class="work-thumb">
<a href="images/sounds/a35_glockenspiel.png" class="image-popup">
<img src="images/sounds/a35_glockenspiel.png" class="img-responsive" alt="a35_glockenspiel">
</a>
</div>
<div class="work-caption">
<h5> 05. glockenspiel </h5>
</div>
</div>
<div class="wow fadeInUp col-md-2 col-md-offset-1 col-xs-6" data-wow-delay="0.4s">
<!-- WORK THUMB -->
<div class="work-thumb">
<a href="images/sounds/a41_celesta.png" class="image-popup">
<img src="images/sounds/a41_celesta.png" class="img-responsive" alt="a41_celesta">
</a>
</div>
<div class="work-caption">
<h5> 06. celesta </h5>
</div>
</div>
<div class="wow fadeInUp col-md-2 col-md-offset-1 col-xs-6" data-wow-delay="0.4s">
<!-- WORK THUMB -->
<div class="work-thumb">
<a href="images/sounds/a42_accordion.png" class="image-popup">
<img src="images/sounds/a42_accordion.png" class="img-responsive" alt="a42_accordion">
</a>
</div>
<div class="work-caption">
<h5> 07. accordion </h5>
</div>
</div>
<div class="wow fadeInUp col-md-2 col-md-offset-1 col-xs-6" data-wow-delay="0.4s">
<!-- WORK THUMB -->
<div class="work-thumb">
<a href="images/sounds/a58_guitar_sarasate.png" class="image-popup">
<img src="images/sounds/a58_guitar_sarasate.png" class="img-responsive" alt="a58_guitar_sarasate">
</a>
</div>
<div class="work-caption">
<h5> 08. guitar </h5>
</div>
</div>
<div class="wow fadeInUp col-md-2 col-md-offset-1 col-xs-6" data-wow-delay="0.4s">
<!-- WORK THUMB -->
<div class="work-thumb">
<a href="images/sounds/a60_piano_schubert.png" class="image-popup">
<img src="images/sounds/a60_piano_schubert.png" class="img-responsive" alt="a60_piano_schubert">
</a>
</div>
<div class="work-caption">
<h5> 09. piano </h5>
</div>
</div>
<div class="wow fadeInUp col-md-2 col-md-offset-1 col-xs-6" data-wow-delay="0.4s">
<!-- WORK THUMB -->
<div class="work-thumb">
<a href="images/sounds/a66_wind_ensemble_stravinsky.png" class="image-popup">
<img src="images/sounds/a66_wind_ensemble_stravinsky.png" class="img-responsive" alt="a66_wind_ensemble_stravinsky">
</a>
</div>
<div class="work-caption">
<h5> 10. wind ensemble </h5>
</div>
</div>
</div>
<!--<p style="margin-bottom: 20px"></p> -->
<div class="wow fadeIn col-md-12 col-sm-12" data-wow-delay="0.2s" style="z-index:0">
<p>
The table below contains listenable excerpts from all three articles.
It is possible to select the initial level of degradation (input SDR) and the displayed evaluation metric.
The postprocessing switch is relevant only for the algorithms inconsistent in the reliable part, which are marked with *.
To listen to results related only to the Audio Declipping Survey, leave the option “Inconsistent restoration” switched on.
The other two options relate to methods presented in the article Audio declipping performance enhancement via crossfading.
</p>
</div>
<div class="wow fadeIn col-md-12 col-sm-12" data-wow-delay="0.4s" style="z-index:0">
<p style="padding-bottom:20px">
The playback can be started by clicking on one of the table cells (the cells turn light blue when the cursor hovers over them).
Your browser must support HTML5 audio player.
Alternativelly, the file path is shown below the player and it can be downloaded by Save Link As ...
</p>
</div>
<div class="chooser" style="margin-top:10px">
<p>
Select input SDR:
<a id="1dB" class="clickable" title="Show input SDR 1 dB." href="#" onclick="Change_inputSDR(0,this.id);return false;">1 dB</a>
<a id="3dB" class="clickable" title="Show input SDR 3 dB." href="#" onclick="Change_inputSDR(1,this.id);return false;">3 dB</a>
<a id="5dB" class="clickable" title="Show input SDR 5 dB." href="#" onclick="Change_inputSDR(2,this.id);return false;">5 dB</a>
<a id="7dB" class="clickable" title="Show input SDR 7 dB." href="#" onclick="Change_inputSDR(3,this.id);return false;">7 dB</a>
<a id="10dB" class="clickable" title="Show input SDR 10 dB." href="#" onclick="Change_inputSDR(4,this.id);return false;">10 dB</a>
<a id="15dB" class="clickable" title="Show input SDR 15 dB." href="#" onclick="Change_inputSDR(5,this.id);return false;">15 dB</a>
<a id="20dB" class="clickable" title="Show input SDR 20 dB." href="#" onclick="Change_inputSDR(6,this.id);return false;">20 dB</a>
<br>
Select table values:
<a id="none" title="Hide result values." href="#" onclick="Change_values(0,this.id);return false;">None</a>
<a id="dSDR" title="Show ∆SDR values." href="#" onclick="Change_values(1,this.id);return false;">∆SDR<sub>c</sub></a>
<a id="PEAQ" title="Show PEAQ ODG values." href="#" onclick="Change_values(2,this.id);return false;">PEAQ ODG</a>
<a id="PEMO_Q" title="Show PEMO-Q ODG values." href="#" onclick="Change_values(3,this.id);return false;">PEMO-Q ODG</a>
<a id="Rnonlin" title="Show Rnonlin values." href="#" onclick="Change_values(4,this.id);return false;">Rnonlin</a>
<br>
Select postprocessing of reliable samples:
<a id="rec" class="clickable" title="Show results of inconsistent restoration." href="#" onclick="Change_postprocessing(0,this.id);return false;">Inconsistent restoration</a>
<a id="RR" class="clickable" title="Show results with replaced reliable samples." href="#" onclick="Change_postprocessing(1,this.id);return false;">Replace Reliable</a>
<a id="CR" class="clickable" title="Show results with crossfaded reliable samples." href="#" onclick="Change_postprocessing(2,this.id);return false;">Crossfaded Replace</a>
</p>
</div>
<div align="center" style="margin-top:20px">
<audio id="audplayer1" controls style="width: 500px" preload="none">
<!-- <source src="sqam/01.ogg" type="audio/ogg"> -->
Warning! Your browser does not support HTML5 audio player.
You will have to download and play the files yourself.
</audio><br/>
Loaded file: <span id="loadedfile1" style="margin-bottom:5pxs">None</span>
</div>
<table class="comptable text-center errtable" class="col-md-12 col-sm-12" cellspacing="0" cellpadding="0"
id="errtable1">
<tr cellpadding="3px", style="border-bottom: 3px double">
<td></td>
<td style="padding-left:20px; padding-right:20px;">01</td>
<td style="padding-left:20px; padding-right:20px;">02</td>
<td style="padding-left:20px; padding-right:20px;">03</td>
<td style="padding-left:20px; padding-right:20px;">04</td>
<td style="padding-left:20px; padding-right:20px;">05</td>
<td style="padding-left:20px; padding-right:20px;">06</td>
<td style="padding-left:20px; padding-right:20px;">07</td>
<td style="padding-left:20px; padding-right:20px;">08</td>
<td style="padding-left:20px; padding-right:20px;">09</td>
<td style="padding-left:20px; padding-right:20px;">10</td>
</tr>
<tr>
<td>Original</td>
<td class="clickable"data-file="sounds/original/a08_violin.wav">X</td>
<td class="clickable"data-file="sounds/original/a16_clarinet.wav">X</td>
<td class="clickable"data-file="sounds/original/a18_bassoon.wav">X</td>
<td class="clickable"data-file="sounds/original/a25_harp.wav">X</td>
<td class="clickable"data-file="sounds/original/a35_glockenspiel.wav">X</td>
<td class="clickable"data-file="sounds/original/a41_celesta.wav">X</td>
<td class="clickable"data-file="sounds/original/a42_accordion.wav">X</td>
<td class="clickable"data-file="sounds/original/a58_guitar_sarasate.wav">X</td>
<td class="clickable"data-file="sounds/original/a60_piano_schubert.wav">X</td>
<td class="clickable"data-file="sounds/original/a66_wind_ensemble_stravinsky.wav">X</td>
</tr>
<tr>
<td>Clipped</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
</tr>
<tr>
<td>C-OMP*</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
</tr>
<tr>
<td>A-SPADE</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
</tr>
<tr>
<td>S-SPADE</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
</tr>
<tr>
<td>ℓ<sub>1</sub> CP</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
</tr>
<tr>
<td>ℓ<sub>1</sub> DR</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
</tr>
<tr>
<td>Rℓ<sub>1</sub>CC CP</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
</tr>
<tr>
<td>Rℓ<sub>1</sub>CC DR</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
</tr>
<tr>
<td>SS EW*</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
</tr>
<tr>
<td>SS PEW*</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
</tr>
<tr>
<td>CSL1*</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
</tr>
<tr>
<td>PCSL1*</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
</tr>
<tr>
<td>PWCSL1*</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
</tr>
<tr>
<td>PWℓ<sub>1</sub> CP</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
</tr>
<tr>
<td>PWℓ<sub>1</sub> DR</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
</tr>
<tr>
<td>DL*</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
</tr>
<tr>
<td>NMF</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
</tr>
<tr style="border-bottom: 3px double">
<td >Janssen</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
</tr>
<tr>
<td>ASS EW*</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
</tr>
<tr>
<td>ASS PEW*</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
<td class="clickable">X</td>
</tr>
</table>
</div>
</div>
</section>
<!-- LISTENING SECTION -->
<section id="work" class="parallax-section">
<div class="container">
<div class="row">
<div class="col-md-12 col-sm-12">
<!-- SECTION TITLE -->
<div class="wow fadeInUp section-title" data-wow-delay="0.2s">
<h2>Individual results</h2>
</div>
<div class="wow fadeIn" data-wow-delay="0.4s" style="margin-bottom:25px">
<p>
The following figure presents supplementary results to the Audio Declipping Survey of the declipping algorithms for each audio excerpt individually.
The respective audio excerpt and objective metric can be selected using the buttons below.
In the plots that follow, algorithms coming from the same family share the same color.
If a method was examined in both the analysis and the synthesis variant,
the analysis variant is graphically distinguished via squared markers.
Other variants (e.g., multiple shrinkage operators in the SS
algorithms or different weights within the CSL family) diamond or triangle markers.
</p>
</div>
<div class="chooser" style="margin-top:10px">
<p>
Select audio excerpt:
<a id="plot_sound_01" title="Show results for audio excerpt 01. violin." href="#" onclick="Change_plot_sound(this.id);return false;">01</a>
<a id="plot_sound_02" title="Show results for audio excerpt 02. clarinet." href="#" onclick="Change_plot_sound(this.id);return false;">02</a>
<a id="plot_sound_03" title="Show results for audio excerpt 03. bassoon." href="#" onclick="Change_plot_sound(this.id);return false;">03</a>
<a id="plot_sound_04" title="Show results for audio excerpt 04. harp." href="#" onclick="Change_plot_sound(this.id);return false;">04</a>
<a id="plot_sound_05" title="Show results for audio excerpt 05. glockenspiel." href="#" onclick="Change_plot_sound(this.id);return false;">05</a>
<a id="plot_sound_06" title="Show results for audio excerpt 06. celesta." href="#" onclick="Change_plot_sound(this.id);return false;">06</a>
<a id="plot_sound_07" title="Show results for audio excerpt 07. accordion." href="#" onclick="Change_plot_sound(this.id);return false;">07</a>
<a id="plot_sound_08" title="Show results for audio excerpt 08. guitar." href="#" onclick="Change_plot_sound(this.id);return false;">08</a>
<a id="plot_sound_09" title="Show results for audio excerpt 09. piano." href="#" onclick="Change_plot_sound(this.id);return false;">09</a>
<a id="plot_sound_10" title="Show results for audio excerpt 10. wind ensemble." href="#" onclick="Change_plot_sound(this.id);return false;">10</a>
<br>
Select objective metric:
<a id="plot_dSDRc" title="Show ∆SDR plot." href="#", onclick="Change_plot_value(this.id);return false;">∆SDR<sub>c</sub></a>
<a id="plot_PEAQ" title="Show PEAQ plot." href="#", onclick="Change_plot_value(this.id);return false;">PEAQ</a>
<a id="plot_PEMO_Q" title="Show PEMO-Q plot." href="#", onclick="Change_plot_value(this.id);return false;">PEMO-Q</a>
<a id="plot_Rnonlin_calc" title="Show Rnonlin plot." href="#", onclick="Change_plot_value(this.id);return false;">Rnonlin</a>
</p>
</div>
</div>
<div class="wow fadeInUp col-md-2 col-sm-0"></div>
<div class="wow fadeInUp col-md-8 col-sm-12" data-wow-delay="0.2s">
<!-- WORK THUMB -->
<div class="work-thumb">
<a id="a.plot" href="images/individual_results/Results_dSDRc_sound_01_styled.png" class="image-popup">
<img id="src.plot" src="images/individual_results/Results_dSDRc_sound_01_styled.png" class="img-responsive mx-auto d-block" alt="Fine Arts">
</a>
</div>
<div class="work-caption">
<h5 id="plot_caption"> Average ∆SDR<sub>c</sub> results, i.e., SDR improvement computed on the clipped samples only.</h5>
</div>
</div>
<div class="wow fadeInUp col-md-2 col-sm-0"></div>
</div>
</div>
</section>
<!-- WORK SECTION -->
<section id="abstract-light" class="parallax-section">
<div class="container">
<div class="row">
<div class="col-md-12 col-sm-12">
<!-- SECTION TITLE -->
<div class="wow fadeInUp section-title" data-wow-delay="0.2s">
<h2>Overall results of the survey</h2>
</div>
<div class="wow fadeIn" data-wow-delay="0.4s" style="margin-bottom:25px">
<p>
In the following figures, the performance of the declipping algorithms is presented.
The comparison is done in terms of four objective metrics —
∆SDR<sub>c</sub> (SDR improvement computed on the clipped samples only),
PEAQ, PEMO-Q, and Rnonlin. In the bar graphs that follow, algorithms
coming from the same family share the same color. If a method
was examined in both the analysis and the synthesis variant,
the analysis variant is graphically distinguished via hatching.
Other variants (e.g., multiple shrinkage operators in the SS
algorithms or different weights within the CSL family) use
gray stippling.
</p>
</div>
<div class="chooser" style="margin-top:10px">
<p style="margin-bottom:1cm">
Select order of the bar graphs:
<a id="Algorithm-sorted" title="Sort values according to the algorithm order." href="#" onclick="Change_sorting_bar_graphs(this.id);return false;">Algorithm-sorted</a>
<a id="Value-sorted" title="Sort values from worst to best." href="#" onclick="Change_sorting_bar_graphs(this.id);return false;">Value-sorted</a>
</p>
</div>
</div>
<div class="wow fadeInUp col-md-12 col-sm-12" data-wow-delay="0.2s">
<!-- WORK THUMB -->
<div class="work-thumb">
<a id="a.dSDR" href="images/main_results/Results_dSDRc.png" class="image-popup">
<img id="src.dSDR" src="images/main_results/Results_dSDRc.png" class="img-responsive" alt="Average dSDRc results.">
</a>
</div>
<div class="work-caption">
<h5> Average ∆SDR<sub>c</sub> results, i.e., SDR improvement computed on the clipped samples only.</h5>
</div>
</div>
<div class="wow fadeInUp col-md-12 col-sm-12" data-wow-delay="0.2s">
<!-- WORK THUMB -->
<div class="work-thumb">
<a id="a.PEAQ" href="images/main_results/Results_PEAQ.png" class="image-popup">
<img id="src.PEAQ" src="images/main_results/Results_PEAQ.png" class="img-responsive" alt="Average PEAQ ODG results.">
</a>
</div>
<div class="work-caption">
<h5>Average PEAQ ODG results. The PEAQ ODG of the clipped signal is depicted in gray.</h5>
</div>
</div>
<div class="wow fadeInUp col-md-12 col-sm-12" data-wow-delay="0.2s">
<!-- WORK THUMB -->
<div class="work-thumb">
<a id="a.PEMOQ" href="images/main_results/Results_PEMOQ.png" class="image-popup">
<img id="src.PEMOQ" src="images/main_results/Results_PEMOQ.png" class="img-responsive" alt="Average PEMO-Q results.">
</a>
</div>
<div class="work-caption">
<h5>Average PEMO-Q ODG results.</h5>
</div>
</div>
<div class="wow fadeInUp col-md-12 col-sm-12" data-wow-delay="0.2s">
<!-- WORK THUMB -->
<div class="work-thumb">
<a id="a.Rnonlin" href="images/main_results/Results_Rnonlin_calc.png" class="image-popup">
<img id="src.Rnonlin" src="images/main_results/Results_Rnonlin_calc.png" class="img-responsive" alt="Average Rnonlin results.">
</a>
</div>
<div class="work-caption">
<h5>Average Rnonlin results.</h5>
</div>
</div>
</div>
</div>
</section>
<!-- WORK SECTION -->
<section id="work" class="parallax-section">
<div class="container">