How MRI Works - Part 3 - Fourier Transform and K-Space
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Published 2022-08-15
Part 1 - NMR Basics: • How MRI Works - Part 1 - NMR Basics
Part 2 - Spin Echo: • How MRI Works - Part 2 - The Spin Echo
Part 4 - The Gradient Echo Sequence : • How MRI Works - Part 4 - The Gradient...
FFT code: github.com/thePIRL/fft-code-for-fun/blob/main/FFT%…
Powerpoint slides from this lecture can be purchased here:
www.patreon.com/thePIRL769/shop/powerpoint-slides-…
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
All Comments (21)
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This channel could be called "Applied 3Blue1Brown"
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I just discovered this series couples of days ago , am so lucky 😂
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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.
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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!!
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The wait was worth it -
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What a coincidence! 2days before my medical imaging systems exam😂 thank you so much. I appreciate the godlike visualisations.
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The best Youtube channel for academic. Thank you so much.
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Best series of videos on MRI. Thank you.
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AWW YEAHHHHHH Part 3 is here fellas
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We need more videos like this, on quantum mechanics and Lagrangian Mechanics. Awesome video!!
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Yes! Awesome, thank you for posting this!
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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.
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Thanks! I have been waiting for this!!
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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!
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Finally, part 3 comes. Thank you for very good lecture of MRI series.
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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! 😄
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Part 4? 😇 the videos are amazing, thanks!
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This is insanely good! Thank you. I just started my section on MRI and this is a life saver
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I want moreeeeee. This videos are amazing!
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I thought I would have to wait for another year. This is awesome thank you so much
