Index Algorithm Decomposition, 117 Donoho and Johnstone denoising, 122 Electrical impedance reconstruction algorithm, 82 Filtered backprojection algorithm, 29, 60 Reconstruction, 117 Ampere's law, 98 Approximate Inverse, 26 Attenuated Radon transform (TM/(u , s)), 75 Inversion, 79 Range conditions, 80 Recovery of attenuation, 80 Band-limited function, 113 Circular Radon transform (Rf(p,r)), 68 Inversion, 72 Range, 73 Set of injectivity, 69 Stability of reconstruction, 72 Coherent interferometric function (X C I N T ), 138 Cone beam transform (Df(a,6)), 38 Inversion formula, 39 Decoherent Frequency (Qd), 139 Length (Xd), 139 Discrete (multi)wavelet transform (W), 121 Electrical Impedance Tomography, 81 Reconstruction algorithm, 82 Stability, 82 Emission tomography, 75 Exponential Radon transform (R^f(u,s)), 76 Inversion formula, 77 Range conditions, 79 Faraday's law of induction, 98 Filter coefficient matrices (P(/c)), 116 Filtered back projection Algorithm, 29, 60 and approximate inverse, 29 Inversion formula, 6 Fourier transform (Tf or / ) , 4 Partial Fourier transform {TsQ)-, 4 Gauss law, 98 Hausdorff metric (5), 111 W W ,K, 144 Holder Space (C n ' s (Q)), 126 Integral equation of the first kind, 108 K(0:b), 50 Kirchhoff migration Function ( J K M ) , 135 In homogeneous medium, 134 In clutter, 137 Lambda tomography, 13 Lattice Sampling (L(7V,P,Q)), 47, 48 Reciprocal lattice (Lg), 50 Limited angle Radon transform (#^(0, s)), 32 Limited angle reconstruction kernel, 36 Limited angle region of interest tomography, 14 Limited data tomography, 10 Exterior tomography, 11 Region of interest tomography, 13 Line (L(p, s)), 3 Linear acoustic equation, 133 Lipschitz function, 126 Magnetic flux leakage, 101 Magnetic flux leakage field ( B E ) , 101 Matrix dilation equation, 116 Maxwell's Equations, 98 Microlocal analysis, 7, 15 Multiresolution analysis, 115 Multiwavelet, 115 Multiwavelet system, 116 157
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