How MRI Works - Part 3 - Fourier Transform and K-Space

How MRI works, Part 3 - The Fourier Transform and k-Space

Powerpoint slides from this lecture can be purchased here:

0:00 - Intro
1:00 - The Sinusoid and phasors
5:48 - Fourier Theory
9:05 - The Fourier Transform and Inverse Fourier Transform
11:10 - Adding phase to our plots
13:42 - Fourier transform of sin(w0t)
17:40 - Hermitian Fourier transforms
19:26 - The Dirac Delta Function

21:00 - Fourier Transform Examples:
21:48 - Decaying Exponential/Lorentzian
29:09 - Square Pulse/Sinc Function
31:08 - Gaussian/Gaussian and Fourier Shift
32:39 - Discrete Signals, Fourier Transforms, and Nyquist
36:12 - The Fast Fourier Transform

40:26 - kSpace
40:48 - t/w and x/k convention
41:55 - Intro to kSpace
48:05 - Hermitian kSpace, half Fourier, and spatial filtering
51:29 - kSpace frequency units
55:08 - FFT organization of kSpace

56:56 - Outro and GRE Teaser

Drinking game: Take a drink every time I say 'notice'

Do I talk too fast in this one?
#some2

[yoyobom]

I just discovered this series couples of days ago, am so lucky 😂

[winterforlife]

After a long wait, the third episode finnaly came. And it was well worth the wait. Cant wait for the next episode in a year.

[monthspregnant]

This channel could be called "Applied 3Blue1Brown"

[lexinwonderland]

I can obviously tell you're a busy guy, but you teased the 4th video too much for me not bug you about it. WE WANT ANOTHER LECTURE ON MRIS, DAMMIT!! your teaching is just too good!!

[apollonyo]

What a coincidence! 2days before my medical imaging systems exam😂 thank you so much. I appreciate the godlike visualisations.

[Lethmyr_]

This is pure gold. I just wished I was smart enough to understand it all..

[Nxck]

I needed to understand k-space for my solid state physics class, a pretty much unrelated context, but your explanation of k-space was so intuitive that I was able to 'translate' to what I needed! Thank you!!

To anyone in the same situation needing a bit more help: at 43:00, we have the physical setup on the right, where the surface represents the complex wavefunction of a given state, and on the left is its corresponding encoding in k-space. For crystals, we have three spatial dimensions instead of two but of course the idea is identical. So, when we look at a point in k-space, we are looking at a wavefunction that oscillates within the unit cell. Due to quantisation, these oscillations must fit an integer number of times within the crystal unit cell size, so our k-space is discretised: k_n = (2 * pi * n) / a.

[t-ew]

I’m a medical student who study physics of medical instruments in high school but never finished it! Now I’m studying it for entertainment in my free time. Thank you for make it all easier for me and many people to learn!

[yazar]

Best series of videos on MRI. Thank you.

[ho]

We need more videos like this, on quantum mechanics and Lagrangian Mechanics. Awesome video!!

[felipemonteiro]

Yes! Awesome, thank you for posting this!

[BIBECHYOUTUification]

The best Youtube channel for academic. Thank you so much.

[bengoodey]

I don`t think I`ve ever been this exited to see a video. Just finished part 2 and really hoped you had made the one about the Fourier Transform. You are really helping me conseptualise MRI and its inner workings! So glad you followed up on your plans, hope the fourth video also gets made and uploaded. Thank you! 😄

[lukec]

I am a new MRI tech and your video series have been invaluable to understanding the NMR phenomenon. It's kind of mind blowing. I think if I watch your videos a few hundred more times I might finally understand it 😜. I can't wait for the next video!

[tinynudges]

Thanks! I have been waiting for this!!

[akekalukardjnaphai]

Finally, part 3 comes. Thank you for very good lecture of MRI series.

[hugodavalos]

This is insanely good! Thank you. I just started my section on MRI and this is a life saver

[finnheinemann]

I thought I would have to wait for another year. This is awesome thank you so much

[electronicbeats]

This was very helpful! I am doing a talk about MRI scanners and I wanted to get an introductory understanding for it, thank you!

[Bozlee]

i’m watching all these before the ARRT exam for extra preparedness