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

ol collelation thlough the Radon transfor'¡r is not yet as attr.active as the
Fouriel tlansforrn apploach. However', thele ale possible advantages of the
Radon transform apploach over fast Fourier. transforrn convolution. The
Raclon tlansfoltn appÌoaches tested in this chapter. ar.e lobust even wlìer
SAR data is corruptecl by noise (also see Murphy [84]), Certain filiering or
scleening plocesses in the Raclor space can be appliecl to efectively reduce
the noise level as a palt of the convolution or. cor.relation pr.ocess. In aclclitiol,
the total number of opelations can be {urther leduced if the Radon
transform of a celtain geometry can be defined by a simple function.
The following noclel test is carlied out using hyperbolas. The test input
data shown in Figule 6.12 are cornposerl of 256 x 256 pixels, ald the apexes
of two hyperbolas are located at (64,71) ancl (-64, 111). The task is to fincl
the coorclinates of these apexes by applyilg correlatior thr.ough the Raclol
transfonn technique ivith a refelence ternplate. A reference template can
be made by a specifiecl shape i,vhich is to be sought in a given irnage, For
this test, the lefelence ternplate is selected as a hyper.bola having its apex
at (0, 11) as shown in Figule 6.13. In the actual operation, the refer.ence
tetr¡rlate is lot necessaly to be pleparecl in the ø-g space. Instead, the
Radon transforrn of a hyperbola is estirnatecl to be an ellipse (the relation
listecl in Table 6.1). A unit value is assignecl to the nearest neighbor.hoocl
pixels along the ellipse il 7r-z domain. Thus tllere is olly one non-zer.o pixel
at each fixed 2-value. Coltelatiol in z-climensiol with this lefer.ence template
in the Raclon space can be accornplished nolv by sirnply shifting the Radon
tlansfoun of the original irnage in the z-dir¡ension. The result of correlation
140