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-- ,': ll"oig)Gs2(r,ro;a) (t2r rvhele O(.) is the olclel of the apploximation error ancl (4.24) oi(r) : ø"(r) ñ'R , (4.25) R(x,y,ziÍo,ao,zo) : l@ - q)2 -+ (a - ao)2 -l (, - (4.26) "o), where Ê ir the unit vectol frorn a scattelel to the source. This apploximation is valid when the fiequency is high enough and A is latge enough to satisfy cf uR 111. ln the SAR case, the value cf øRhas at rrost an order of 10-3. Eq.(a.23) indicates that the backscattered wavefielcl can be expressed using an integlal ovel alì possible scatterers on the glound. The integlancl is the procluct of the complex backscattelilg coeficient ai(r), the wave propagation ternr exp{-i2utlc}f R2, and, the lineal frecluency-
4.4 The Inversion The equation Eq.(a.23), clelived in the previous section, inclicates that the inverse scattering problem associated s'ith the SAR theory leduces to a problem of estirnating the cornplex backscatteling coefficient oi(r) fr:orn the backscatteled wavefielcl Ue(.r¡,y¡,261c.l) as observecl along the line y6 : so : 6. Inversion of Eq.(a.23) can utilize a spatial Fourier tlansfolmation to clerive a sirnple relation between the obselvecl clata and the backscattering coefÊcient in the /-fr clomail. As rlentioned in the plevious section, the forwalcl founula, Eq.(4.23), is sinilar to the conventional expression of the range-compressecl SAR siglal except for the spreading fa ctot lf R2 tenn. Most conventional SAR processor-s use exp{-i 2a,,,8/c} as the azimuth inpulse-response function. It has l¡een known that it is clifÊcult to find an explicit Fouliel transfolm forr¡ula for this frrnctiorr. If, horvever', olly a 1/,R terrn is ilcluded, it becomes to obtain an explicit Fourier transforur relationship with respect to ¿0. T1ìe Fouliel tt'ansfortl of tlre function exp\*i2uRlcj f R is a Hankel function of the seconcl kincl (Magnus ancl Obelhettinger' [71], p.ll8). Moreovei', the fir'st-olcler asymptotic approxirnation of the Hankel function recluces the result to the kelnel of the Foulier t¡:ansform as shown by Eq.(4..3) in Appendix A. The integland in Eq. (4.24), ltowever', is a squale of the Green's function. To ovelcome this problem, a modified function can be introducecl il an analogous rnanner to tlie seismic Born inversioli scheme ({ol instance, trq.(10) of Bleistein 78
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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]).
Page 45 and 46: Table 2.6: ERS-1 SAR pelfolmance re
Page 47 and 48: Table 2.7: JtrRS-1 olbit pararnetel
Page 49 and 50: Table 2.9: Chalactelistics of OPS o
Page 51 and 52: Table 2.11: Specifications of Racla
Page 53 and 54: Chapten 3 Review of Digital SAR Pro
Page 55 and 56: ,I Figule 3.1: Raclar' L¡earn geom
Page 57 and 58: I L-=J}"no Figure 3.2: Geouretry fo
Page 59 and 60: vhich is the clistance across the a
Page 61 and 62: vlrere ø6 is a angular center fi'e
Page 63 and 64: à1 äl (a) /1T. or^l - r+ (b) I à
Page 65 and 66: a,pploxirnated by l2p sinl(I - ltl)
Page 67 and 68: -s(cu) is rewlitten as s@¡ - !"-,r
Page 69 and 70: cliscussecl later il this sectio¡r
Page 71 and 72: Ïon = _2 (V(ro) .V(¿o)+ R(ro) .A(
Page 73 and 74: : Range Walk : Range Curvatule : Ra
Page 75 and 76: olbital SAR is given by Ion = -'#{t
Page 77 and 78: is constant cluling the receiving p
Page 79 and 80: a at f¡r
Page 81 and 82: 'rvith a foulula developed il this
Page 83 and 84: Chapter 4 Theoretical Development 4
Page 85 and 86: 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: elorv that sulface. In genetal, sul
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 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
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C-l¡ancl SAR irnagery ovel this al
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Figure 6.8: Radon transform of ailb
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in the irnage space ancl the Iine i
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ERS- 1 N U 0 rl 0o |lO + ,¡l r.l p
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6.2,3 Correlation Using The Radon T
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Since the inside of the squale blac
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Figule 6.12: Model test for correla
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thlough the Radon tlansfolm is shor
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Figure 6.15: Airborne C-band SAR da
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distinct points can be cliscelnerl
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Figure 6.18: Correlation output thr
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6.3 Merging of Multiple SAR Image D
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in Figure 6.19 tvhich is a clilect
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Figure 6.20: Additive irnages rvith
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Figule 6.22: Subtractive images rvi
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(1) select a clirection to be enhan
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Figure 6.24: Lnage obtained through
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6.3.4 Principal Components Analysis
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Table 6.2: Con'elation coeffrcielt
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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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