10.pdf - K-space Traversal continued Vikram Kodibagkar...

K-space Traversal (continued)
Vikram Kodibagkar

Data collection and “k-space”
k
x
=
γ G
RO
t
k
y
=
γ G
PE
t
PE
k
x
k
y
The k-space data : real and imaginary ‘channels’
Each channel is a 3d data set : Intensity as a function of k
x
and k
y
i.e. F(k
x
,k
y
) {actually F(t, G
PE
)}
Int
k
y
k
x

k
x
k
y
|kspace|
k-space

Discrete Fourier Transform
The image I(x,y) is the 2D discrete Fourier transform of
the k-space data F(k
x
,k
y
)
FT
k-space F (k
x
,k
y
)
MR image I(x,y)
Note:The 2 channel k-space data gives rise to 2-channel image data.
The image we see is the magnitude image (sqrt(R
2
+I
2
))
2 2
1 1
)
2
0 0