Mathematical Methods in Image Processing and Inverse Problems

Description

IPIP 2018, Beijing, China, April 21–24 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