Multi-bang Regularisation and Applications

Lead Research Organisation: University of Manchester
Department Name: Mathematics

Abstract

The goal of the project will be to study so-called multi-bang regularisation methods for imaging problems in which the image is known to only take on a finite number of possible values. The student will consider both theoretical questions related to convergence of algorithms, as well as practical applications. Initial focus areas will be the combination of total-variation regularisation with multi-bang, and application to the emission tomography problem.

Publications

10 25 50
publication icon
Holman S (2020) SPECT with a multi-bang assumption on attenuation in Inverse Problems

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509565/1 01/10/2016 30/09/2021
1916298 Studentship EP/N509565/1 04/08/2017 31/03/2021 Philip Richardson
 
Description An algorithm for joint recovery of multi-bang( takes only finitely many known values) attenuation and radiation source density from SPECT data has been proposed with promising results from synthetic data. If the attenuation is multi-bang and made up of piecewise constant convex regions, with some continuity constraints on the radiation source density, we can show that unique recovery of both attenuation and source density is possible. Furthermore the multi-bang regulariser we have had most success with is a weakly convex variation of that initially proposed and this has lead to further convergence criteria.
Exploitation Route The joint reconstruction algorithm could be parallelised to work on GPUs for faster computation. Currently the joint reconstruction algorithm is 2D and this could be extended to the 3D case. The unique recovery for convex multi-bang attenuation could potentially be extended to the case where the radiation source density is not assumed to be continuous. In particular this could be used in the Identification problem for SPECT. The techniques are not limited to the human body and could see applications in material science with proper parameter tuning.
Sectors Aerospace, Defence and Marine,Manufacturing, including Industrial Biotechology,Pharmaceuticals and Medical Biotechnology,Security and Diplomacy