Mathematical Methods in Image Processing and Inverse Problems

This book contains eleven original and survey scientific research articles arose from presentations given by invited speakers at International Workshop on Image Processing and Inverse Problems, held in Beijing Computational Science Research Center, Beijing, China, April 21-24, 2018. The book was dedicated to Professor Raymond Chan on the occasion of his 60th birthday. The contents of the book cover topics including image reconstruction, image segmentation, image registration, inverse problems and so on. Deep learning, PDE, statistical theory based research methods and techniques were discussed. The state-of-the-art developments on mathematical analysis, advanced modeling, efficient algorithm and applications were presented. The collected papers in this book also give new research trends in deep learning and optimization for imaging science. It should be a good reference for researchers working on related problems, as well as for researchers working on computer vision and visualization, inverse problems, image processing and medical imaging.

Contenu
Point Spread Function Engineering for 3D Imaging of Space Debris using a Continuous Exact $\ell_0$ Penalty (CEL0) Based Algorithm.- An Adjoint State Method for a Schr"odinger Inverse Problem.- On A New Diffeomorphic Multi-modality Image Registration Model and Its Convergent Gauss-Newton Solver.- Fast Algorithms for Surface Reconstruction from Point Cloud.- A Total Variation Regularization Method for Inverse Source Problem with Uniform Noise.- AUTOMATIC PARAMETER SELECTION BASED ON RESIDUAL WHITENESS FOR CONVEX NON-CONVEX VARIATIONAL RESTORATION.- Total Variation Gamma Correction Method for Tone Mapped HDR Images.- On the Optimal Proximal Parameter of an ADMM-like Splitting Method for Separable Convex Programming.- A new initialization method for neural networks with weight sharing.- The Shortest path amid 3-D polyhedral obstacles.- Multigrid Methods for Image Registration Model based on Optimal Mass Transport.