Key Information

The topic of the summer school is Algorithms and Theory for Tomographic Image REconstruction. It covers all analytic aspects of image reconstruction and includes the most advanced topics in the field. However, no iterative algorithms will be covered.

From Sunday evening to Saturday morning, we will be offering a choice of 30 lecture hours or 23 lecture hours with 9 hours of computer labs. Lectures will be given by five internationally renowned researchers, in an informal setting.

We anticipate about 40 attendees (with a strict maximum of 50). Although the target audience is students and post-docs, it is open to any interested parties. We will provide certificates of attendance for all who request them, and certificates of achievement for those who successfully complete an optional final exam.

The summer school will take place in le Clos des Capucins, a former abbey in the village of Yenne, not far from Chambéry, France. We strongly encourage all participants to stay at the summer school site and to take all meals on-site (as much as dietary restrictions allow). Contact us if you have any special needs.

 

Motivation

Image reconstruction from projections plays a key role in medical and industrial tomography.  Analytical methods in tomography have long played a major role in applications. They model the problem as an integral equation such as the Radon transform or one of its generalisations, for which closed form solutions are known, which allow fast numerical implementations. In contrast, iterative methods in tomography use a discrete model of the imaging problem and solve the resulting equations by means of iterative algorithms. Over the past twenty years, iterative methods have progressively replaced analytical methods in positron emission tomography, in single-photon emission computed tomography and to a lesser but growing extent also in X-ray CT. As a result, a growing number of scientists involved in image reconstruction are unaware of recent advances in analytical methods or even of its basic principles. Yet, even when iterative algorithms are found optimal for a specific application, critical issues such as identifiability (is the solution unique?) and stability (is the solution stable?) can only be adressed using analytical methods. Such issues are important when optimizing data acquisition; the role of analytic methods in tomography extends therefore well beyond the actual calculation of a solution. The objective of the ATTIRE summer school is to offer an up-to-date and in-depth overview of this fascinating field.

 

 

Is this Summer School too mathematical for me?

Probably not! The prerequisites are a first course in linear algebra, calculus of 2 or 3 variables (jacobian of change of variables such as polar to rectangular), notions of Fourier series, Fourier transforms, including the convolution of two functions.

This background material is  normally covered in the first three years of most undergraduate programs in engineering, physics, mathematics and computer science.

The content of this summer school is equivalent to course material given at the masters or PhD level in fields such as medical physics, applied mathematics, imaging science, computational science, biomedical engineering.

 

 

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