Medical Image Processing - Digital Signal Processing for Medical Imaging Using Matlab - page 74

Fig. 4.4 Original spectrum and the logirthmic spectrum of the MRI image (with origin) in the
middle

(refer Appendix) of the function F ( q ) is given as

∞

f ( r ) = 2 π qF ( q ) J 0 ( 2 π qr ) (4.1)

0

where,

π

1
π

J 0 ( q ) = cos ( q sin (φ)) (4.2)

0

2. Thus the hankel transformation is applied to the function F ( q ) to obtain f ( r ) .

3. The values of F ( r ) are treated as the polar representation of the spatial domain

.
4. For the 2D-filter specification shown in the Fig. 4.6 , the spatial domain of filter
obtained using the direct method (2D-IDFT) and the hankel transformation are

F ( r ,θ) for all the angle θ