ch 8 mri Fourier Transforms in Magnetic Resonance Imaging

define function

establishes a relationship between numbers

define transform

establishes a relationship between functions

define fourier transform

Mathematical procedure to separate the frequency and phase components of a time-varying or spatially varying signal from the amplitudes as a function of time

_____ is used to generate the spectrum from the FID and is essential to most imaging techniques.

Fourier transform

Spatial Frequency Domain

a dimension of the Fourier transform space (like k-space) having units of inverse distance.

what is k- space??

a matrix that stores raw data from an MRI scan

what does k space represent

the spatial frequency information of an object in two or three dimensions. It is used to create the final image

give an example of a high spatial frequency object.

A bone-soft tissue interface

do sharp or smooth objects contain more extremely wide ranges and higher frequencies?

sharp

A sharp-edged object might be an MR signal of a fluid-filled cyst: true or false

true

Orthogonality

the generalization of the geometric notion of perpendicularity

ex of orthogonality

2 lines that are perpendicular to each other or intersect at a right angle

The Fourier transform and its inverse MUST always exist and they must be reversible in order to form what??

an mri image

what is the 3rd fundamental property of the Fourier Transform

periodicity

what does periodicity do

relates the periodic behavior of the FT with its inverse

The transformation from the MRI signal to the MR image itself is actually an ___ Fourier Transform

inverse

The Fourier transform (FT) has two parts:

1. real

2. imaginary

Spin Echo is not symmetrical sometimes due to:

motion (ex- blood flowing in a vein)

Sampling (aka- Digitization)

the process of interrogating a signal at regular intervals for the purpose of computation

(the MRI computer takes the data of the continuous MR signal and converts the data into discrete numbers.)

alias

false recognition. Wrap-around artifact. The result of inadequate signal sampling.

Remedy for Aliasing on MRI can be compensated for by:

➢ enlarging the field of view (FOV)

➢ using pre-saturation bands on areas outside the FOV

➢ anti-aliasing software

➢ switching the phase and frequency directions

➢ use a surface coil to reduce the signal outside of the area of interest