Restoring a picture using the FOURIER TRANSFORM! #VeritasiumContest

Title:

Description:

In this video we save a beautiful picture of Veritasium-Derek from distortion and explain the Fourier Transform, all in 60 seconds. It was created by the three KTH students Albin, Kevin & Jonas and is our take at a simple explanation of the concept Fourier Transform and why it is useful. The example was coded in Matlab and code can be distributed upon request if you want to play around with it yourself.

Thank you for watching our submission to the #VeritasiumContest !

Credits:

Music: “Moon and Star” by Wintergatan
This track can be downloaded for free at www.wintergatan.net
Free License to use this track in your video can be downloaded at www.wintergatan.net

Picture of Derek is from: https://www.tubefilter.com/wp-content/uploads/2015/11/derek-muller-veritasium-snatoms-1920x1131.jpg

Further studies:

If you want an in-depth explanation of the theory behind the Fourier transform we'll hand over to 3Blue1Brown who has already done an excellent video on the topic: https://youtu.be/spUNpyF58BY

The periodic noise in the example is a sinusoidal signal with extreme frequency and amplitude to magnify the visual effects of the disturbance and simplify the filtering process. It is not something commonly found in real life signal processing applications and signal/image processing can often be a much trickier topic and the subject to master level studies in engineering.

Script:

Instead of using this complicated formula, we are going to explain Fourier transform by demonstration, to propose that it is a tool that opens up a new dimension of analysis.

If you look at these two signals, which one do you think is the simplest?
Technically, it is the same signal, a combination of three periodic signals, sinusoids with different frequencies, but represented differently as functions of both time and frequency. The transform between these domains is the Fourier transform. In the frequency domain we can easily identify the frequencies of the sinuses, while the time signal is a lot messier.

Let’s study an example where this new perspective can be useful: a picture that’s distorted by a periodic noise that we want to restore to its original quality. The pixel values of this image can be seen as a signal on which we can use the fourier transform as before. Now we can identify that the noise is located at this frequency, which is clearly different from the picture frequencies and can be filtered out, making the picture of Veritasium flawless again!

Contact:
jonas.cederberg@gmail.com

Old titles:
Everyone CAN understand the FOURIER TRANSFORM #VeritasiumContest
Restoring a picture using the FOURIER TRANSFORM! #VeritasiumContest

YouTube url:	https://youtu.be/bpn3DEULv8g
Created:	18. 1. 2023 06:54:18

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Restoring a picture using the FOURIER TRANSFORM! #VeritasiumContest