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Since the inside of the squale blacket is the Raclon tlansfomr of /(ø, y), the equation results in rvhere e@, ") : li otr, "l Gþt, z - z') rtz' (6.10) Tltelefole, tlvo-rlinensional convolution in (ø, g) domain reduces to only oneclimensiollal convolution in the Radon transforrl clornain (p, z), that is rvhele fþ,ù P4 ¡*"osP+F*,G f (x,,fi P!+ R.î. !@,a ) - Fb,z) F@,2) Glp,2 ) (6.e) (6.1 1) (6.12) ancl x", clenotes two-climensional convolution in c- and g-climension, while +, denotes ole-clirnensional convolution in z-clirnension. Siuilar-ly, the Radon tlansfou¡ of trvo-dimensioral colrelatior can be provecl to be ¡ 6", s P!+ r ø"c (6.13) rvhele S", clenotes trvo-dilnensional correlation in ¿- and y-dirnension, rvhile @, clenotes one-climensional colrelation in z-dimersion. In the above clerivatin it rvas shorvn that the Radon transfolrn of trvodirrensional couvolution ol correlatiol respectively reduces to one-climensional convolution or cou'elation. As regarcls computational efficiency, convolution 139
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 <strong>SAR</strong> 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
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INVERSION OF SYNTHETIC APERTUR,E R,
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ñr^-- ltoN. J00NG suN '¿i¡r"r os
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I heleby declale that I am tlie sol
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plot of the maximum amplitude of th
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Contents Abstract Acknowledgements
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6.3.1 Introduction ..151 6.3.2 Digi
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5.1 Florv chart fot the proposecl i
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List of Tables 2,1 Seasat SAR senso
Page 17 and 18:
List of Notations cr squint angle P
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tist of Abbreviatíons SAR Syntheti
Page 21 and 22:
The objectives of this thesis rnay
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Ground Range l;l 2 sin0 Figure 1.2:
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ol'cler to evaluate its full aclvan
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algolithrn extlacts the complex bac
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successful as expected. Thele ale,
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eú ø1. [103]). Similal clevelopme
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aerial plìotogl'aphy ovel the area
Page 35 and 36:
2.2 Spaceborne SAR Systems 1) SEASA
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tlie basis of a distinctive dlainag
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set fol selectecl aleas, useful for
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3) ERS-I The first European rernote
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Table 2.4: ERS-I Ðieterle [104]).
Page 45 and 46:
Table 2.6: ERS-1 SAR pelfolmance re
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Table 2.7: JtrRS-1 olbit pararnetel
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Table 2.9: Chalactelistics of OPS o
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Table 2.11: Specifications of Racla
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Chapten 3 Review of Digital SAR Pro
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,I Figule 3.1: Raclar' L¡earn geom
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I L-=J}"no Figure 3.2: Geouretry fo
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vhich is the clistance across the a
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vlrere ø6 is a angular center fi'e
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à1 äl (a) /1T. or^l - r+ (b) I à
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a,pploxirnated by l2p sinl(I - ltl)
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-s(cu) is rewlitten as s@¡ - !"-,r
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cliscussecl later il this sectio¡r
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Ïon = _2 (V(ro) .V(¿o)+ R(ro) .A(
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: Range Walk : Range Curvatule : Ra
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olbital SAR is given by Ion = -'#{t
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is constant cluling the receiving p
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a at f¡r
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'rvith a foulula developed il this
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Chapter 4 Theoretical Development 4
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developed and cliscussed by several
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vhere u (r,ro; u) : I U 1r,ro,t)e-i
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wheÌe k':frf a¡cl lc -_ uf us ant
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4) there is relative motion of ante
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o =løo, 0, 0) Figure 4.1: Schemati
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elorv that sulface. In genetal, sul
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4.4 The Inversion The equation Eq.(
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*'here % is a platfolrn velocity an
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The trq.(a.36) cannot be used dilec
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vhele Àl is a tvavenurnbel collesp
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2-D FFT o(,b,;ø) Intelpolation in
Page 107 and 108: ¡nE 0$r-sEc, ¡3 I IrlÊ [18- 5EC
Page 109 and 110: 5.2 Digital Simulation Digital sirn
Page 111 and 112: Table 5.2: Moclel palametels fol di
Page 113 and 114: signal and the leconstructe
Page 115 and 116: (3 È. e tc o) o -tl a Slant Range
Page 117 and 118: that the inversiol method can accor
Page 119 and 120: (n t0 Ê) 0c (lr) Figure 5.6: Seasa
Page 121 and 122: 5.3 Processing of Real SAR Data A s
Page 123 and 124: squâre pixel rvith clir¡ension of
Page 125 and 126: Aziurutì (n Þ !d !D gc Figule 5.1
Page 127 and 128: (n 5 F Þ tq Figu.e 5.11: Reconst.u
Page 129 and 130: over tlìe 2.4 inches as shol¡l i'
Page 131 and 132: Ø Þ :J m (a) (b) ^a ctl _= a"r ro
Page 133 and 134: Chapter 6 SAR fmage Enhancement for
Page 135 and 136: 1) hoiv can the tlends of lineament
Page 137 and 138: 6.2 Determination of Geological Str
Page 139 and 140: Coolclinates for the image space an
Page 141 and 142: Figure 6.2: Point, lines, and hyper
Page 143 and 144: scatteter (e.g. coller leflectols,
Page 145 and 146: Figure 6.5: CCRS's airboure C-band
Page 147 and 148: C-l¡ancl SAR irnagery ovel this al
Page 149 and 150: Figure 6.8: Radon transform of ailb
Page 151 and 152: in the irnage space ancl the Iine i
Page 153 and 154: ERS- 1 N U 0 rl 0o |lO + ,¡l r.l p
Page 156 and 157: 6.2,3 Correlation Using The Radon T
Page 160 and 161: Figule 6.12: Model test for correla
Page 162 and 163: thlough the Radon tlansfolm is shor
Page 164 and 165: Figure 6.15: Airborne C-band SAR da
Page 166 and 167: distinct points can be cliscelnerl
Page 168 and 169: Figure 6.18: Correlation output thr
Page 170 and 171: 6.3 Merging of Multiple SAR Image D
Page 172 and 173: in Figure 6.19 tvhich is a clilect
Page 174 and 175: Figure 6.20: Additive irnages rvith
Page 176 and 177: Figule 6.22: Subtractive images rvi
Page 178 and 179: (1) select a clirection to be enhan
Page 180 and 181: Figure 6.24: Lnage obtained through
Page 182: 6.3.4 Principal Components Analysis
Page 185 and 186: Table 6.2: Con'elation coeffrcielt
Page 187 and 188: Figure 6.27: The PCA frrst componen
Page 189 and 190: the geological surface lilearrent f
Page 191 and 192: ackscatte.i'g coefficiert can be cl
Page 193 and 194: Appendices A. Derivation of Forward
Page 195 and 196: B. Derivation of Inversion Formula
Page 197 and 198: C. Derivation using the Method of S
Page 199 and 200: F[eferences [1] Ahmed, S., \Vallen,
Page 201 and 202: [20] Curlis, J.D,, Flost, V.S., Del
Page 203 and 204: [43] Holn, R., 1988, E-SAR - The ex
Page 205 and 206: [65] Lotrelrl, O., 1990, Dopplel ce
Page 207 and 208: [87] Pye, 8.G., Nalch'ett,4.J., anc
Page 209:
[111] \,Vu, C., Balkan,8., I(arplus
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