INVERSION OF SYNTHETIC APERTUR,E R,ADAR (SAR) - MSpace ...

Coolclinates for the image space and the Raclon space usecl in this thesis
ale as follorvs. The image space is defined by (c,g) coor.clinate as shorvn in
Figure 6.1. The origin of ¿ is at the center of ver.tical axis, n4rile the oligin of
y is at the left-rnost pixel. The Radon space is clefinecl by (p,") coor.dinate.
Slope of a line is defilled by ¡r, which is zero if parallel to z-axis, ancl positively
increases clockivise as shorvn in Figure 6.1. The coordinate z is defined by
the interception of a line at ¿ = 0. Given this coordinate convention, the
Radon transfortn is given by
úþt'z) :
(Radon [88]). The notatiol
'¡;_';,;:,',i,1 , - p.)¿*¿, (6 1)
S@,fi ë4,üfti,2) (6,2)
rvill be usecl to ildicate tliat the function /(ø, y) ancl ü(p, z) ale lelated by
the Radon tlansfolm in Eq.(6.1).
Various ploperties of the Radou transforrrr wele surnmarized in Deans
[25] (pp.65-95), ¿ncl Dulrani and Bisset [28]
(p.1181, Table 1). Three Raclor
transfolrn pails ale surnmalizecl in Table 6,1 as exarnples,
An example depictecl in Figures 6.2 ancl 6.3 illustrate the Radon tr.altsfoln.l
pairs of a point, lines ancl an hyper.bola. The point, trvo str.aight lines, and
ole hypelbola are respectively napped onto a lile, poiuts, ancl ellipse in the
Raclon tlansfolm space (p-z space) as il Figure 6.3. hr t,his exanple, one can
easily lealize that the contribution to Radon transform of an isolated point
120