A discrete Ginzburg-Landau functional for regularised tomographic image reconstruction

Abstract

Tomographic imaging has a wide range of applications including in medicine and in industry because of its non-destructive nature. Ideally, accurate images can be retrieved using high-quality fully sampled computed tomography (CT) scan data. In practice, images are reconstructed from noisy subsampled data. One way to acquire good quality reconstructions is to encode prior information on expected image structures.

In this project, we consider discrete (graph) Ginzburg-Landau (GL) functional regularisation to express such prior information. We study the use of graph GL regularisation in binary image denoising and binary CT image reconstruction. For the binary image denoising problem, we examine the influence of various graph definitions on the performance of the graph GL functional. For the tomographic image reconstruction problem, we compare graph GL regularisation with two other well-known methods, total variation (TV) regularisation and simultaneous iterative reconstruction technique (SIRT), in various noise levels and downsampled projection settings. Graph GL regularisation shows good performance with limited and high-noise data. Moreover, we collect our own CT scan data, and investigate how it might be applied in practical scenarios.