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54 Cards in this Set
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What is fourier transform

The 1D Fourier transform is a mathematical procedure that allows a signal to be decomposed into its frequency components.


What 3 parameters are needed to describe a sine wave with fourier transform

amplitude
frequency phase 

How is frequency determine



How is magnitude determined



What is the fourier transform

The Fourier transform is a mathematical procedure that decomposes a signal into a sum of sine waves of different frequencies, phases and amplitude.


By knowing frequency, amplitude and phase of each sine wave, is possible to reconstruct the signal (inverse Fourier transform).

yes


What tends to have a higher amplitude low or high frequency

low frequency


What is the right to left direction in MR

X


What is changing when moving from right to left

the rows


What type of frequency have the greatest change in intensity

low spatial frequencies


Do high spatial frequencies have low amplitude

yes


What describes the basic shape of the image

low spatial frequencies


What must be done to create a 2d image

2D fourier transform


How is a 2D fourier transform created

first it is done in one direction(X ...right to left)


What is the frequency domain



Is there a frequency domain in the X and Y direction

yes


Look and see how low spatial frequencies have the greatest change in intensity.

Note that the big waves are low frequency and have the biggest change in intensity


Note how the high spatial frequency have lower amplitudes

small little waves (redline)


What describes the general shape of an MR image

General shape of the image is described by low spatial frequencies: this is also true with MRI images


What is the 2nd step of the 2D fourier transform

The second step of 2D Fourier transform is a second 1D Fourier transform in the orthogonal direction (column by column, Oy), performed on the result of the first one


What is the image that can be created as a result of a fourier transform in the X and Y direction



What do the horizontal and vertical axis correspond to

Horizontal and vertical axis correspond to horizontal and vertical spatial frequencies


What determines the pixel intensity

Pixel intensity corresponds to the amplitude (or magnitude) of frequency component


What does the color correspond to

Color corresponds to the phase of frequency component


What are the 3 things encoded in a fourier plane

Horizontal and vertical axis correspond to horizontal and vertical spatial frequencies
Pixel intensity corresponds to the amplitude (or magnitude) of frequency component Color corresponds to the phase of frequency component. 

What is this called

fourier plane


What are the 3 components of a fourier plane



where is the MR signal stored

The readout MR signal is stored in Kspace which is equivalent to a Fourier plane.


How do you go from a Kspace to an image

To go from a kspace data to an image requires using a 2D inverse Fourier Transform


How do you go from a Kspace to an image



What is required to go from K space to image formation

To go from a kspace data to an image requires using a 2D inverse Fourier Transform.


Are frequencyencoding and phaseencoding done so that data is spatially encoded by differences in frequency and phase, amenable to analysis by Fourier transform

yes


In kspace what is the horizontal spatial frequency replaced by

Kx


In Kspace what is the vertical spacial frequency replaced by

Ky coordinates


What does the Kspace coordinate system look like



Where does the Kspace start to fill in following the 90° RF pulse + Sliceselection gradient :

location at origin (center) of kspace


Where does the K space fill if there is negative and strong phase encoding gradient

moves to the lower bound of kspac


What line is filled in following a 180 RF pulse and the slice selection gradient

moves to the opposite location


Repetition for each line with increasing phaseencoding gradient strength (negative to positive intensity).

The amount of gradient phase change between adjacent line is constant. This results in a sequential (line by line) filling of kspace from top to bottom.


What determines the K space location in the Kx and Ky coordinate system

The kspace location (kx and ky coordinates) of data is governed by the accumulated effect of gradient events and excitation pulses


Where is the begining of the sequence in K space

The initial RF excitation pulse (with the sliceselection gradient) is the beginning of the sequence: location is at the center of kspace.


What governs the next movement in Kspace

the phase encoding gradient


What determines what direction K space will go in the Y direction

The greater the net strength of the phaseencoding gradient (or the longer the gradient is on), the farther from the kspace origin the data belong, in the upper direction if the gradient is positive or in the lower direction if the gradient is negative. As the duration of phaseencoding gradient is most often constant, the strength of the phaseencoding gradient governs the location on the vertical axis (kycoordinate).


What if there is a strong positive phase encoding gradient

It will move up


What happens if there is a negative phase encoding gradient

it will move down


What determines how far from the K space origin it will go
2 
The greater the net strength of the phaseencoding gradient (or the longer the gradient is on), the farther from the kspace origin the data belong,


After the gradient moves up or down (Ydirection bc of phase encoding gradient), where does it go now

right or left depending on the frequency encoding gradient


If the phase encoding gradient was negative (previous example) and there is a strong positive frequency encoding gradient which direction doese K space fill

to the right


If the phase encoding gradient was negative (previous example) and there is a NEGATIVE frequency encoding gradient which direction doese K space fill

to the left


What determines the direction of Kspace filling during the frequency encoding gradient

The longer the frequencyencoding gradient is on (or the greater the net strength of the gradient is), the farther from the kspace origin the data belong, in the right direction if the gradient is positive or in the left direction if the gradient is negative. As the strength of the frequencyencoding gradient is most often constant, the duration of the frequencyencoding gradient governs the location on the horizontal axis (kxcoordinate)


What happens following the 180 RF pulse

if fills on the opposite side of K space


What is the order of a standard spin echo sequence

90 pulse
phase encoding frequency encoding 180 degree pulse 

What is the order of filling in K space

90 pulse center
phase encoding  up or down frequency encoding  L or R 180 pulse flip to other side 

How does phase encoding gradient strength dictate how the kspace is filled ing

Repetition for each line with increasing phaseencoding gradient strength (negative to positive intensity). The amount of gradient phase change between adjacent line is constant. This results in a sequential (line by line) filling of kspace from top to bottom.
