Restoring a picture using the FOURIER TRANSFORM! #VeritasiumContest

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

Further studies:

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:

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

[prof_dos_anjos]

I don't know about the contest results but it certainly is one of the best one-minute videos on YT.

[camillah]

Thanks for the great explanation! Hope to see more soon xoxo

[Fabelot]

This will save new students the hours of reading and scratch wounds in the scalp that I had to go through to get this

[amortalbeing]

where can I find the details about this context? the original noisy image? and the accompanying Matlab code?
I'd like to give that a try myself.

[KingZ]

This quality and your subscriber count do not match at all xD
Really well done video. You deserve way more fame