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liecl out usilg the CCRS's ailbolne C-band and ERS-1 SAR clata over the Suclbuly Basin. Results of tlle Radot tr.ansforu analysis clemonstlate that it is very efficient ancl efective for cleter.rnining clominant tlends of surface lineaments fiorn SAR data. Holever, the l.adar. look dilection bias shoulcl be carefully analyzed in the plocess. The second application is correlation usilg the Radon transform for. locatirg geologic featules of specifiecl shape in a givel SAR image. The Raclon tlalsform of trvo-dimensional convolution ancl couelation ar.e derivecl il this study, an
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
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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
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List of Notations cr squint angle P
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tist of Abbreviatíons SAR Syntheti
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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
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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]).
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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
Page 87 and 88: vhere u (r,ro; u) : I U 1r,ro,t)e-i
Page 89 and 90: wheÌe k':frf a¡cl lc -_ uf us ant
Page 91 and 92: 4) there is relative motion of ante
Page 93 and 94: o =løo, 0, 0) Figure 4.1: Schemati
Page 95 and 96: elorv that sulface. In genetal, sul
Page 97 and 98: 4.4 The Inversion The equation Eq.(
Page 99 and 100: *'here % is a platfolrn velocity an
Page 101 and 102: The trq.(a.36) cannot be used dilec
Page 103 and 104: vhele Àl is a tvavenurnbel collesp
Page 105 and 106: 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: 6.2 Determination of Geological Str
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 158 and 159: Since the inside of the squale blac
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
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the geological surface lilearrent f
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ackscatte.i'g coefficiert can be cl
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Appendices A. Derivation of Forward
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B. Derivation of Inversion Formula
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C. Derivation using the Method of S
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F[eferences [1] Ahmed, S., \Vallen,
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[20] Curlis, J.D,, Flost, V.S., Del
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[43] Holn, R., 1988, E-SAR - The ex
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[65] Lotrelrl, O., 1990, Dopplel ce
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[87] Pye, 8.G., Nalch'ett,4.J., anc
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[111] \,Vu, C., Balkan,8., I(arplus
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