Audio Restoration Project

Brief Overview

Audio restoration has become an integral part of digit age and it's tasks range from restoring old recordings to reducing noise in modern audio tracks. An important task of audio restoration algorithms is to remove random clicks in an audio signal which can be done using several methods, namely, AR Method, Cubic Interpolation and Median Filtering. The current project demonstrates two kinds of "click" removal mechanisms:

1. Median Filtering
2. Cubic Interpolation

The current project uses an original audio track which is then degraded by adding high amplitudes at random points. The file new_clean.wav is an original audio track which does not have any degradations or "clicks". Henceforth, the term "clicks" will be used to denote degradations in the tracks. The file new_degraded.wav is the degraded track in which distinct clicks can be heard at random points. cubic_clean.wav is the audio track that was restored using cubic interpolation. clean_median.wav is the audio track that was restored using median filtering.

Getting started

The project is divided into 3 main files:

1. Median_Flter_Restoration.py
2. Cubic_Audio_Restoration.py
3. unit_test.py

Dependencies

To run any of the files, please check whether your machine has the following dependencies:

1. wave
2. tqdm
3. matplotlib
4. pandas
5. scipy
6. playsound
7. pymatreader
8. alive_progress
9. sys
10. subprocess

The following dependencies can be installed on a local machine using the following command - pip install <dependency_name> A list of dependencies is available in the file requirements.txt

Cloning the Project

The project can be cloned to a local machine via a terminal window using the command:

git clone https://github.com/radiobenzene/Audio_Restoration.git

Median Filtering

Let us detail the algorithm for median filtering:

1. Read input track - new_degraded.wav
2. Read .mat file (Matlab) threshold_bk.mat that contains a list of points where clicks exist. For convenience, we shall denote them as "indicators".
3. Convert the .mat file to an array. As a Matlab file is read as a "Dictionary" type, we must convert it into an "Array"
4. Get the indices of those points where the .mat file has clicks, i.e. the indicator gets a value of 1
5. Set a window length for the median filtering
6. Define a certain constant length, i.e. delta, which is an offset of window length. This value will help us apply the median filtering only around the specified window
7. Apply the median filter, i.e Sorting the points which lie within the window range and calculating the median value.
8. Substitue those values which have been filtered back into the track
9. Write the track to a new file - clean_median.wav

Cubic Interpolation

Let us detail the algorithm for cubic interpolation:

1. Read input track - new_degraded.wav
2. Read .mat file (Matlab) threshold_bk.mat that contains a list of points where clicks exist. For convenience, we shall denote them as "indicators".
3. Convert the .mat file to an array. As a Matlab file is read as a "Dictionary" type, we must convert it into an "Array"
4. Get the indices of those points where the .mat file has clicks, i.e. the indicator gets a value of 1
5. Get the track length and convert the track length into a range, starting from [0,len(track)]
6. From the degraded track, first remove the indices where a click has been detected, then remove the data points corresponding to these indices.
7. Apply the out-of-the-box function CubicSpline() which will interpolate those points.
8. Substitue those values which have been filtered back into the track
9. Write the track to a new file - clean_cubic.wav

Implementation specifics

The following command must be typed in to run the median filtering algorithm on a local machine:

python3 Median_Flter_Restoration.py --run

or

python3 Median_Flter_Restoration.py -r

The following command must be typed in to run the cubic interpolation algorithm on a local machine:

python3 Cubic_Interpolation_Algorithm.py --run

or

python3 Cubic_Interpolation_Algorithm.py -r

The command extensions for the project are as follows:

python3 Median_Flter_Restoration.py --run
python3 Median_Flter_Restoration.py --mse
python3 Median_Flter_Restoration.py --plot
python3 Median_Flter_Restoration.py --diff
python3 Median_Flter_Restoration.py --theme
python3 Median_Flter_Restoration.py --sound
python3 Median_Flter_Restoration.py --unit
python3 Median_Flter_Restoration.py --help

A list of features can be found by typing:

python3 Median_Flter_Restoration.py --help

The user may also type the initial letter of each command extension, i.e -h, -m, -p, -d, -t, -s, -u and -h respectively. The command extension --run runs the project, creating a restored audio file and displaying the execution time. For the cubic interpolation algorithm, replace Median_Flter_Restoration with Cubic_Interpolation_Algorithm. The two programs share command extensions.

Plots

Plots for the Median Filtered Audiotrack

These are the plots The plots can be printed using the following command

python3 Median_Flter_Restoration.py --plot

Plots for the Cubic Interpolated Audiotrack

These are the plots The plots can be printed using the following command

python3 Cubic_Audio_Restoration --plot

The Plot for a degraded audiotrack

Plot for the original clean audiotrack

Plot for a restored audiotrack using median filtering

Plot for a restored audiotrack using cubic interpolation

Unit testing

To run unit tests for the medianFilter() function, type in the command

python3 Median_Flter_Restoration.py --unit

This generates 5 tests on different tests sets with a minimum list length of 10 and a maximum of 20052. The user may also run 2 separate unit tests by executing the file unit_test.py using the following command

python3 unit_test.py

After every unit test, an OK is printed if the test is passed, otherwise NOT OK is printed, along with the number of passed and failed tests. The unit test feature is only available for median filtering. The separate file unit_test.py uses Python's unittest module and runs only 2 tests.

Performance Metrics

The Mean Sqaured Error, or the MSE, was calculated for the restored track and the original track to quantify the improvement on the audiotrack. The following command can be used to print the MSE:

python3 Median_Flter_Restoration.py --mse

To get the MSE of the cubic interpolated audiotrack, the following command must be used:

python3 Cubic_Audio_Restoration --mse

Mean Squared Error

The MSE for the median filtered track is 0.27 and the MSE for the Cubic Interpolated track is 0.30. The difference between the MSEs of the 2 tracks can be printed using the following command:

python3 Median_Flter_Restoration.py --diff

The comparison of the MSEs can be visualized on the following graph:

The comparison of the MSEs with respect to a change in window length can be visualized on the following graph:

Execution Time

The execution time for a track restored using a median filter is 7.6637 seconds. The execution time for a track restored using a cubic interpolation is 17.7269 seconds The execution time for a track restored using an AR Model is 62.729 seconds

The comparison of the execution time for a median filter can be visualized on the following graph:

The comparison of the execution time for a median filter with respect to a change in window length can be visualized on the following graph:

Themes

An interesting addition to the project is the option of changing the theme of the loader which can be done using the extension --theme or -t.

Credits

Written by Uditangshu. Project for the 5C22 Computational Methods Module. Trinity College Dublin. 2022.