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54 Cards in this Set
- Front
- Back
What is fourier transform
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The 1D Fourier transform is a mathematical procedure that allows a signal to be decomposed into its frequency components.
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What 3 parameters are needed to describe a sine wave with fourier transform
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amplitude
frequency phase |
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How is frequency determine
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How is magnitude determined
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What is the fourier transform
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The Fourier transform is a mathematical procedure that decomposes a signal into a sum of sine waves of different frequencies, phases and amplitude.
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By knowing frequency, amplitude and phase of each sine wave, is possible to reconstruct the signal (inverse Fourier transform).
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yes
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What tends to have a higher amplitude low or high frequency
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low frequency
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What is the right to left direction in MR
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X
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What is changing when moving from right to left
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the rows
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What type of frequency have the greatest change in intensity
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low spatial frequencies
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Do high spatial frequencies have low amplitude
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yes
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What describes the basic shape of the image
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low spatial frequencies
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What must be done to create a 2d image
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2D fourier transform
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How is a 2D fourier transform created
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first it is done in one direction(X ...right to left)
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What is the frequency domain
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Is there a frequency domain in the X and Y direction
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yes
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Look and see how low spatial frequencies have the greatest change in intensity.
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Note that the big waves are low frequency and have the biggest change in intensity
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Note how the high spatial frequency have lower amplitudes
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small little waves (redline)
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What describes the general shape of an MR image
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General shape of the image is described by low spatial frequencies: this is also true with MRI images
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What is the 2nd step of the 2D fourier transform
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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
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What is the image that can be created as a result of a fourier transform in the X and Y direction
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What do the horizontal and vertical axis correspond to
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Horizontal and vertical axis correspond to horizontal and vertical spatial frequencies
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What determines the pixel intensity
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Pixel intensity corresponds to the amplitude (or magnitude) of frequency component
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What does the color correspond to
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Color corresponds to the phase of frequency component
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What are the 3 things encoded in a fourier plane
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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. |
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What is this called
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fourier plane
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What are the 3 components of a fourier plane
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where is the MR signal stored
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The readout MR signal is stored in K-space which is equivalent to a Fourier plane.
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How do you go from a K-space to an image
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To go from a k-space data to an image requires using a 2D inverse Fourier Transform
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How do you go from a K-space to an image
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What is required to go from K space to image formation
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To go from a k-space data to an image requires using a 2D inverse Fourier Transform.
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Are frequency-encoding and phase-encoding done so that data is spatially encoded by differences in frequency and phase, amenable to analysis by Fourier transform
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yes
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In k-space what is the horizontal spatial frequency replaced by
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Kx
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In K-space what is the vertical spacial frequency replaced by
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Ky coordinates
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What does the K-space coordinate system look like
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Where does the K-space start to fill in following the 90° RF pulse + Slice-selection gradient :
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location at origin (center) of k-space
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Where does the K space fill if there is negative and strong phase encoding gradient
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moves to the lower bound of k-spac
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What line is filled in following a 180 RF pulse and the slice selection gradient
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moves to the opposite location
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Repetition for each line with increasing phase-encoding gradient strength (negative to positive intensity).
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The amount of gradient phase change between adjacent line is constant. This results in a sequential (line by line) filling of k-space from top to bottom.
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What determines the K space location in the Kx and Ky coordinate system
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The k-space location (kx and ky coordinates) of data is governed by the accumulated effect of gradient events and excitation pulses
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Where is the begining of the sequence in K space
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The initial RF excitation pulse (with the slice-selection gradient) is the beginning of the sequence: location is at the center of k-space.
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What governs the next movement in K-space
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the phase encoding gradient
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What determines what direction K space will go in the Y direction
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The greater the net strength of the phase-encoding gradient (or the longer the gradient is on), the farther from the k-space 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 phase-encoding gradient is most often constant, the strength of the phase-encoding gradient governs the location on the vertical axis (ky-coordinate).
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What if there is a strong positive phase encoding gradient
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It will move up
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What happens if there is a negative phase encoding gradient
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it will move down
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What determines how far from the K space origin it will go
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The greater the net strength of the phase-encoding gradient (or the longer the gradient is on), the farther from the k-space origin the data belong,
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After the gradient moves up or down (Y-direction bc of phase encoding gradient), where does it go now
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right or left depending on the frequency encoding gradient
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If the phase encoding gradient was negative (previous example) and there is a strong positive frequency encoding gradient which direction doese K space fill
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to the right
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If the phase encoding gradient was negative (previous example) and there is a NEGATIVE frequency encoding gradient which direction doese K space fill
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to the left
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What determines the direction of K-space filling during the frequency encoding gradient
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The longer the frequency-encoding gradient is on (or the greater the net strength of the gradient is), the farther from the k-space 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 frequency-encoding gradient is most often constant, the duration of the frequency-encoding gradient governs the location on the horizontal axis (kx-coordinate)
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What happens following the 180 RF pulse
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if fills on the opposite side of K space
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What is the order of a standard spin echo sequence
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90 pulse
phase encoding frequency encoding 180 degree pulse |
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What is the order of filling in K space
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90 pulse -center
phase encoding - up or down frequency encoding - L or R 180 pulse flip to other side |
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How does phase encoding gradient strength dictate how the k-space is filled ing
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Repetition for each line with increasing phase-encoding 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 k-space from top to bottom.
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