Image Reconstruction for 3D Lung Imaging - Department of Systems ...

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λ = 10 −9 λ = 10 −8 λ = 10 −7 λ = 10 −6 λ = 10 −5 λ = 10 −4 Figure 7.14: Profiles of TV solutions at the 7 th iteration (convergence). Showing effect of using different λi values in equation 7.38. Dotted line is generating contrast, solid line is TV solution. λi ∈ [10 −9 ,10 −4 ] computational requirements. 113
Figure 7.15: Four layer tank used for 3D reconstructions. Red patches are the 32 electrodes in 2 layers. Phantom contrast are the blue elements which are only in the second layer (between z=1 and z=2). Simulated water depth is full vertical extent of tank. Error Norm 0 2 4 6 8 10 12 14 16 18 20 Iteration Figure 7.16: Convergence of 3D PD-IPM algorithm. (a) z=0 (bottom) (b) z=1 (c) z=2 (d) z=3 (e) z=4 (top) Figure 7.17: Slices of 3D reconstructions for Iteration 1. No noise added. (a) z=0 (bottom) (b) z=1 (c) z=2 (d) z=3 (e) z=4 (top) Figure 7.18: Slices of 3D reconstructions for Iteration 8. No noise added. 114
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Enhancements in Electrical Impedanc
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Acknowledgements I would like to de
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3.5 3D Considerations . . . . . . .
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Bibliography 127 VITA 135 vii
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4.8 GCV curves for different priors
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7.15 Four layer tank used for 3D re
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Discrete Variables • I is the mat
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as opposed to anatomical imaging. W
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to know how various alternative con
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to noise however both algorithms pr
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Chapter 2 Forward Problem 2.1 Descr
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there are two primary types in EIT.
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impedance, σ(�x,t) + jω(�x,t)
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elying on a variational statement.
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with Y11 = −Y12 − Y13, Y22 =
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2.3.1.3 Derivation of Linear Interp
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with Ci being the following column
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Substitution of 2.24 into 2.21 yiel
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where the superscript identifies th
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2.3.3.4 Numerical Implementation of
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is selected, measurements are taken
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measurements of which only 104 are
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Chapter 3 Reconstruction The proces
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where the Jacobian is � H = T −
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The condition number of a matrix is
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2. As λ goes to zero, the un-regul
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6. Evaluate a stopping rule. For ex
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Finally Adler and Guardo define the
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3.5 3D Considerations In EIT it is
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Chapter 4 Objective Selection of Hy
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initial conductivity x = ∆σ/σ0.
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λ=0.0008 λ=0.0302 λ=0.0616 λ=6.
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4.3.3 Generalized Cross-Validation
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1. simulated data, generated using
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GCV 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0
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a hyperparameter selection method,
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1. Heuristic selections of hyperpar
Page 75 and 76: human lung data. Keywords: regulari
Page 77 and 78: fields when reconstructing in 2D [1
Page 79 and 80: i and integrating across element j
Page 81 and 82: 5.2.5 Nodal Gaussian Filter The Gau
Page 83 and 84: Quantitative figures of merit are r
Page 85 and 86: (a) Rdiag BR=.236, SNR=.332 (b) Fil
Page 87 and 88: plane located halfway between the e
Page 89 and 90: models that are difficult or imposs
Page 91 and 92: 6.1 Introduction EIT attempts to ca
Page 93 and 94: 6.2.1 Image Reconstruction In order
Page 95 and 96: Aligned, fig 6.2(a) Planar Zigzag Z
Page 97 and 98: of reconstructions were calculated
Page 99 and 100: case normalized to the first and la
Page 101 and 102: Resolution (BR) Image Radial Positi
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Page 105 and 106: Planar and Planar-offset configurat
Page 107 and 108: Chapter 7 Total Variation Regulariz
Page 109 and 110: on the conductivity vector, σ, whi
Page 111 and 112: a regularization penalty term a muc
Page 113 and 114: etween primal and dual optimal poin
Page 115 and 116: The optimization problem min x 1 2
Page 117 and 118: PD-IPM Algorithm ψ(σ) = 1 2 �F(
Page 119 and 120: (a) First step, TV solution. BRTV =
Page 121 and 122: Iteration 1 (a) Iteration 4 (d) Ite
Page 123 and 124: (a) L 2 solution with 2.5% AWGN, fi
Page 125: (a) i=1 (b) i=2 (c) i=3 (d) i=4 (e)
Page 129 and 130: can be solved with the algorithm. T
Page 131 and 132: Appendix: Variability in EIT Images
Page 133 and 134: where H is the Jacobian or sensitiv
Page 135 and 136: (a) AσˆL = 33% (b) Aσ ˆL = 51%
Page 137 and 138: Figure A.4: Reconstructions with ho
Page 139 and 140: Figure A.7: Reconstructions with no
Page 141 and 142: [15] Barber DC, Brown BH, Applied p
Page 143 and 144: [49] Frerichs I, Hahn G, Hellige G,
Page 145 and 146: [83] Kunst PWA, Vonk Noordegraaf A,
Page 147 and 148: [116] Vauhkonen M, Lionheart WRB, H
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