IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Total Variation Regularization in Tomography

  • Jan. 28, 2011, 2:20 p.m. LeConte 312
  • Feb. 4, 2011, 2:20 p.m. LeConte 312

Abstract

In one of the current projects of the IMI, the aim is to reconstruct the spatial distribution of heavy atom clusters in a carrier material from a tilt series of STEM (scanning transmission electron microscopy) images. This can be considered as an application of limited angle tomography which is well known to lead to ill-posed problems. It seems reasonable to utilize the total variation for regularization, an approach which has recently become popular due to the advances in compressed sensing and image processing.

In the first talk I want to present the application and to give a concise introduction to the underlying mathematics, in particular back projection and Fourier methods, and to review some recent publications on these topics.

In the second talk I concentrate on the algebraic reconstruction technique, present numerical results, discuss the introduction of additional constraints, show how to solve the arising convex optimization problems, and consider possible alternative approaches.

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