Sách Time-domain Reconstruction Methods for Ultrasonic Array Imaging

1 Introduction 1
1.1 Basic Ultrasonic Imaging Concepts . 3
1.1.1 Ultrasonic Transducers 4
1.1.2 Ultrasonic Image Presentation Methods 5
1.1.3 Wave Modes of Elastic Waves 10
1.1.4 Ultrasonic Measurement Congurations 11
1.2 Conventional Array Imaging . 13
1.3 Problem Formulation . 21
1.3.1 The Image Formation Model 22
1.4 Thesis Contributions and Relation to Earlier Work 24
1.5 Outline of the Thesis . 27
1.6 Financial Support 29
I Ultrasound Theory and Modeling 31
2 Ultrasound Wave Propagation 33
2.1 The Acoustic Wave Equation 34
2.2 Green's Functions 35

2.3 Boundary Conditions and Related Integrals 37
2.3.1 The Rayleigh Integral 37
2.3.2 The Rayleigh-Sommerfeld Integral . 39
2.3.3 The Kirchhho Integral . 40
2.4 The Convolution Integral 41
3 The Spatial Impulse Response 43
3.1 Analytical Solutions for some Canonical Transducer Types 44
3.1.1 The Point Source . 44
3.1.2 The Line Source . 45
3.1.3 The Circular Disc 46
3.2 Sampling Analytical Spatial Impulse Responses 48
3.3 The Pressure Field 50
3.4 A Numerical Method for Computing Spatial Impulse Responses 51
3.A The Rectangular Source . 56
3.B An Algorithm for Computing SIRs in Immersed Solids 59
4 A Discrete Linear Model for Ultrasonic Imaging 63
4.1 Model Assumptions . 64
4.2 A Linear Imaging Model . 65
4.3 A Discrete Two-dimensional Model . 68
II Methods based on Delay-and-sum Focusing 73
5 The Synthetic Aperture Focusing Technique 75
5.1 The SAFT Algorithm 77
5.2 Performance of The Synthetic Aperture Focusing Technique . 79
5.2.1 Spatial Undersampled Broadband Data 80
5.2.2 Finite Sized Transducers and Lateral Resolution . 84
5.3 Matrix Formulation of the SAFT Algorithm 85
5.4 Matched Filter Interpretation 88
5.5 Remarks 88

6 Real Aperture Array Imaging 91
6.1 Conventional Narrowband Transmit Beamforming Analysis . 92
6.2 Broadband Transmit Beamforming with Finite Sized Array
Elements . 93
6.3 Parallel Receive Beamforming 98
III Bayesian Ultrasonic Image Reconstruction 101
7 Ultrasonic Image Reconstruction Methods 103
7.1 Bayesian Image Reconstruction . 106
7.1.1 Assigning Prior Probability Density Functions | The
Maximum Entropy Principle 109
7.1.2 The Optimal Linear Estimator . 114
7.1.3 The Optimal Beamformer with Exponential Prior 116
7.2 Focusing as an Inverse Problem . 116
7.2.1 Singular Value Decomposition Inversion 118
7.2.2 Tikhonov Regularization . 118
7.2.3 The Maximum Likelihood Estimator 120
7.3 Concluding Remarks . 121
7.A Some Matrix Derivations . 122
7.A.1 Equivalence of MAP and Linear MMSE Estimators . 122
7.A.2 Performance of the Linear MMSE and MAP Estimators122
8 Applications 125
8.1 Experimental Equipment 126
8.2 Ultrasonic Synthetic Aperture Imaging . 127
8.2.1 The Monostatic Propagation Matrix 127
8.2.2 Lateral Resolution and Finite Sized Transducers . 130
8.3 Parallel Array Imaging 137
8.3.1 The Propagation Matrix for Parallel Receive Imaging 137
8.3.2 The Optimal Linear Estimator . 139





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