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source: International Centre for Theoretical Sciences 2015年3月10日

Advanced Instructional School on Theoretical and Numerical Aspects of Inverse Problems

URL: https://www.icts.res.in/program/IP2014

Dates: Monday 16 Jun, 2014 - Saturday 28 Jun, 2014

Description

In Inverse Problems the goal is to determine the properties of the interior of an object from the object response measured on the boundary, when the object is probed by electrical, acoustic or other means. Such problems arise in medical imaging, oil exploration, non-destructive testing and other fields. Determining the object properties corresponds to finding the non-constant coefficients of a partial differential equation (PDE) from the values, on the boundary of the region, of the solutions of the PDE. These problems may also be interpreted as the inversion of non-linear maps or transforms. The solution of these inverse problems requires harmonic analysis, PDE theory, numerical methods for PDEs, and custom designed inversion transforms and schemes.

Basics (Distribution theory) 1:29:45

Basics (Statistical techniques) 1:14:24

Introduction to Inverse problems 53:15

Basics (Control Theory) 1:00:34

Introduction to Inverse problems 13:40

Microlocal analysis of generalized Radon transforms 1:03:08

Generalized Radon transforms in tomography 1:06:44

Microlocal analysis of generalized Radon transforms 1:06:54

Generalized Radon transforms in tomography 1:00:10

Inverse problems in Riemannian and Lorentz geometry 1:03:11

Carleman estimates/Hyperbolic inverse problems 1:01:37

Microlocal analysis of generalized Radon transforms 59:07

Generalized Radon transforms in tomography 1:01:27

Inverse problems in Riemannian and Lorentz geometry 58:51

Carleman estimates/Hyperbolic inverse problems 1:05:24

Microlocal analysis of generalized Radon transforms 1:03:50

Generalized Radon transforms in tomography 57:58

Inverse problems in Riemannian and Lorentz geometry 1:04:17

Inverse problems in Riemannian and Lorentz geometry 58:11

Numerics Survey 59:17

Introduction to the numerical solution of inverse problems 1:01:49

Hybrid Imaging 59:40

Inverse problems in Riemannian and Lorentz geometry 55:17

Introduction to the numerical solution of inverse problems 1:03:53

Hybrid Imaging 59:23

Inverse problems in seismic/radar imaging 59:46

Hybrid Imaging 1:00:23

Inverse problems in seismic/radar imaging 51:54

Numerical methods in inverse problems 56:43

Hybrid Imaging 1:02:22

Inverse problems in seismic/radar imaging 56:39

Calderon problem 54:55

Numerical methods in inverse problems 55:14

Hybrid Imaging 1:04:00

Numerical methods in inverse problems 48:01

Inverse problems in seismic/radar imaging 1:00:01

Carleman estimates 1:10:03

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