INVERSE PROBLEMS AND IMAGING (Code 363) SEMESTER: SECOND CONTACT: DR W R B LIONHEART (M/P6) CREDIT RATING: 10
 Aims: To introduce inverse and ill-posed problems and their application to industrial and medical imaging problems Objectives of Course: On successful completion of this module students will understand the basic theory of regularization for ill-posed problems, and its application to a number of medical and industrial problems. Pre-requisites for this module: 111, 112, 113/CT102, 157, 151, 215 Co-requisites for this module: Course Description: In science and engineering one often needs to infer the material properties of an object from some physical measurement.  Typical examples are industrial and medical imaging one applies for example ultra sound, X-rays or an electromagnetic field to an object, makes measurements on the outside and then attempts to form an image of the inside.  These problems are typically ill-posed in the sense that the mapping taking data to image is discontinuous, and numerically reconstruction algorithms tend to be unstable unless one makes sufficient assumptions, such as smoothness, about the image.  This course covers both the theory and practice of the process of reconstructing an image from measured data.  The course will be illustrated by practical examples including visits to experimental groups at UMIST, and will include numerical examples illustrated with MATLAB programs. Teaching Mode: 2 Lectures per week 1 Tutorial per week Private Study: 4 hours per week Recommended Texts: Beretro & Boccacci, Introduction to Inverse Problems in Imaging  Taraantola, Inverse Problem Theory Natterer & Wubbeling, Mathematical Methods in Image Reconstruction Lionheart & Arridge, Methods for Solving Non-linear Inverse Problems Assessment Methods: Coursework:  30% Coursework Mode:  Group case study of an applied problem. Examination:  70% Examination is of 2 hours duration at the end of the Second Semester
 No of lectures: Syllabus 5 Introduction to linear ill-posed discrete inverse problems, Tikhonov regularization and the singular value decomposition. 5 Example from integral equations, image processing, and CT 4 Reconstruction algorithms for CT. 4 The inverse conductivity problem - ill-posedness and nonlinearity. 4 Methods for solving nonlinear inverse problems.
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