About the HD-Tomo Tomography Project

About the HD-Tomo Project

High-Definition Tomography

Tomography is the science of "seeing through objects." Physical signals - waves, particles, currents - are sent through an object from many different angles, the response of the object to the signal is measured, and an image of the object's interior is reconstructed by means of a computer. Tomography is behind some of the most important and profound scientific discoveries of all times: The interior structure and processes of the Earth, Moon and Sun and the first maps showing the location of simple mental processes in the human brain are notable examples.

The Goal

A decisive factor behind the human brain's unrivalled success with 3D reconstruction is the ability to use prior information - an organized accumulation of experience with similar objects. The goal of the HD-Tomo project is to accomplish this on a computer: We use state-of-the-art mathematics and scientific computing to develop the enabling technology for next-generation tomographic reconstruction algorithms that can incorporate a variety of prior information, and thus achieve major improvements in the details and reliability of high-definition reconstructions - sharper images with reliable details.

The Challenges

Prior information comes in many different forms (e.g., constraints, statistical priors, or "catalogues" of trustful images) and the challenge is to design new mathematical methods that incorporate all this information in an optimal way. An additional challenge is how to represent and perform computations with the huge amounts of data in 3D reconstructions.

The Ingredients

We will consider a variety of problems, based on both linear and nonlinear models, and using integral equations as well as partial differential equations. We will also consider a variety of reconstruction methods, including analytical inversion methods, methods based on a variational formulation, and sampling methods in a Bayesian formulation. To incorporate all available prior information in various forms, we will replace classical algorithms built on ad-hoc assumptions with new algorithms based on models and methods that take their basis in the actual prior information in a given problem.

The Focus

We focus on development of mathematical and numerical algorithms in an applied mathematics research environment that has close ties to information technology and high-performance computing, and the research will incorporate close collaborations with scientific and industrial users of tomography. Our computational methods must be targeted to a range of computational platforms including personal computers and small-scale clusters that are standard equipment in labs today. To ensure the dissemination of our results outside the applied mathematics community we will also publish joint papers with the application experts.

The Impact

By means of our new methods, scientists/engineers will be able to advance the use of tomographic methods in a wide range of applications: Our research will have impact on, e.g., security scanners for passengers and cargo, oil/gas/geothermal energy exploration, process and production monitoring for safety and quality, X-ray and neutron scattering in materials science, and medical applications such as dementia diagnostics, screening, and surgery aid. But our results are not restricted to tomography - rather, we expect that our results will have a broader impact on the general field of applied and computational mathematics relating to imaging problems.

For more information, see the pdf file with the project presentation slides.