Mathematical Methods in Image Processing and Inverse Problems

Preface
Contents
Point Spread Function Engineering for 3D Imaging of Space Debris Using a Continuous Exact ell0 Penalty (CEL0) Based Algorithm
1 Introduction
2 CEL0-Based Optimization Model
3 Development of the Algorithm
4 Numerical Results
5 Conclusions and Future Work
References
An Adjoint State Method for An Schrödinger Inverse Problem
1 Introduction
2 Our Proposed Approach Based on the Adjoint State Method
3 Some Implementation Details
3.1 Inversion with Full Measurements
3.2 Inversion with Finite Number of Measurements
3.3 A Cascadic Initialization Approach
4 Numerical Examples
4.1 A Constant Model
4.2 A Non-constant Model
4.3 Discontinuous Models
5 Conclusion
References
Multi-modality Image Registration Models and Efficient Algorithms
1 Introduction
2 Review of Related Models
3 The New Model
3.1 Data Fitting
3.2 Regularization
3.3 Invertibility
4 The Solution Algorithm
4.1 Discretization
4.2 Optimization Method for the Discretized Problem (17)
5 Numerical Results
5.1 Example 1
5.2 Example 2
6 Conclusions
References
Fast Algorithms for Surface Reconstruction from Point Cloud
1 Introduction
2 Proposed Algorithms
2.1 Semi-implicit Method (SIM) to Minimize E2
2.2 Augmented Lagrangian Method (ALM) to Minimize E1
2.3 Connection Between SIM and ALM Algorithms
3 Numerical Implementations, Experiments and Effects of Parameters
3.1 Implementation Details
3.2 Numerical Experiments of 2D and 3D Point Clouds
3.3 Choice of Parameters for ALM and the Effects
4 Conclusion
References
A Total Variation Regularization Method for Inverse Source Problem with Uniform Noise
1 Introduction
2 Total Variation Regularization for Inverse Source Problem
3 Primal-Dual Approach
3.1 Chambolle-Pock's First-Order Primal-Dual Algorithm
3.2 Minimax Problem
3.3 Subproblem for r
3.4 Subproblem for ξ
4 Numerical Results
5 Conclusion
References
Automatic Parameter Selection Based on Residual Whiteness for Convex Non-convex Variational Restoration
1 Introduction
2 Related Work
3 The Class of CNC Variational Models
4 Residual Whiteness
5 The Proposed Algorithmic Framework
6 Numerical Examples
7 Conclusions
References
Total Variation Gamma Correction Method for Tone Mapped HDR Images
1 Introduction
1.1 The Contribution
2 The Proposed Model
2.1 The Algorithm
3 Experimental Results
4 Concluding Remarks
References
On the Optimal Proximal Parameter of an ADMM-like Splitting Method for Separable Convex Programming
1 Introduction
2 Preliminaries
3 The Positive Indefiniteness of (1.11) with τ>0.5
4 A Prediction-Correction Explanation of (1.11)
5 Investigation of the Quadratic Term (vk-tildevk)T G(vk-tildevk)
6 Convergence
7 The Optimality of τ=0.5
8 Convergence Rate
9 Conclusions
References
A New Initialization Method for Neural Networks with Weight Sharing
1 Introduction
2 Neural Networks and CirCNN Implementations
2.1 Single Layer Structure
2.2 CirCNN Networks
3 The Xavier/Kaiming Initialization and its Limitation
4 A New Initialization for Fully Connected Layers
4.1 Our Initialization Conditions for Fully Connected Layers
4.2 New Initialization for CirCNN Fully Connected Layers
4.3 Numerical Experiments
5 Conclusion and Future Work
References
The Shortest Path AMID 3-D Polyhedral Obstacles
1 Introduction
2 New Algorithm
2.1 Geodesics on Polyhedrons
2.2 Structure of the Shortest Path
2.3 Optimal Path
2.4 Numerical Scheme
2.5 Algorithm
2.6 Complexity Analysis
3 Numerical Examples
4 Polyhedron with Holes
5 Future Work
References
Multigrid Methods for Image Registration Model Based on Optimal Mass Transport
1 Introduction
2 Image Registration Model Based on Optimal Mass Transport
2.1 Image Registration
2.2 Optimal Mass Transport Model
2.3 Monge-Ampère Equation
3 Finite Difference Discretization
3.1 Standard 7-Point Stencil Discretization
3.2 Semi-Lagrangian Wide Stencil Discretization
3.3 Mixed Discretization
4 Multigrid Methods
4.1 Policy-MG Iteration
4.2 MG for 7-Point Stencil
4.3 MG for Mixed Discretization
5 Numerical Results
5.1 Multigrid for Standard 7-Point Stencil Discretization
5.2 Multigrid for Mixed Discretization
6 Conclusion
References
Author Index