IPIP 2018, Beijing, China, April 21–24 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