Mathematical and Statistical Methods for Imaging
About this Title
Habib Ammari, Ecole Normale Supérieure, Paris, France, Josselin Garnier, Université Paris VII, Paris, France, Hyeonbae Kang, Inha University, Incheon, Korea and Knut Sølna, University of California, Irvine, Irvine, CA, Editors
Publication: Contemporary Mathematics
Publication Year 2011: Volume 548
ISBNs: 978-0-8218-5289-7 (print); 978-0-8218-8227-6 (online)
This volume contains the proceedings of the NIMS Thematic Workshop on Mathematical and Statistical Methods for Imaging, which was held from August 10–13, 2010, at Inha University, Incheon, Korea.
The goal of this volume is to give the reader a deep and unified understanding of the field of imaging and of the analytical and statistical tools used in imaging. It offers a good overview of the current status of the field and of directions for further research. Challenging problems are addressed from analytical, numerical, and statistical perspectives. The articles are devoted to four main areas: analytical investigation of robustness; hypothesis testing and resolution analysis, particularly for anomaly detection; new efficient imaging techniques; and the effects of anisotropy, dissipation, or attenuation in imaging.
Graduate students and research mathematicians interested in mathematical and statistical aspects of image processing.
Table of Contents
- Josselin Garnier – Use of random matrix theory for target detection, localization, and reconstruction
- Pierre Garapon – Resolution limits in source localization and small inclusion imaging
- Souhir Gdoura and Lili Guadarrama Bustos – Transient wave imaging of anomalies: A numerical study
- Gang Bao, Junshan Lin and Faouzi Triki – Numerical solution of the inverse source problem for the Helmholtz equation with multiple frequency data
- Mikyoung Lim and SangHyeon Yu – Reconstruction of the shape of an inclusion from elastic moment tensors
- John C. Schotland – Path integrals and optical tomography
- Kiwan Jeon and Chang-Ock Lee – Denoising of $B_z$ data for conductivity reconstruction in magnetic resonance electrical impedance tomography (MREIT)
- Daniel G. Alfaro Vigo and Knut Sølna – Time reversal for inclusion detection in one-dimensional randomly layered media
- Elie Bretin and Abdul Wahab – Some anisotropic viscoelastic Green functions
- Habib Ammari, Elie Bretin, Josselin Garnier and Abdul Wahab – Time reversal in attenuating acoustic media