On sparse forward solutions in non-stationary domains for the EIT imaging problem

Panagiotis Kantartzis, Panos Liatsis

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In the forward EIT-problem numerical solutions of an elliptic partial differential equation are required. Given the arbitrary geometries encountered, the Finite Element Method (FEM) is, naturally, the method of choice. Nowadays, in EIT applications, there is an increasing demand for finer Finite Element mesh models. This in turn results to a soaring number of degrees of freedom and an excessive number of unknowns. As such, only piece-wise linear basis functions can practically be employed to maintain inexpensive computations. In addition, domain reduction and/or compression schemes are often sought to further counteract for the growing number of unknowns. In this paper, we replace the piece-wise linear with wavelet basis functions (coupled with the domain embedding method) to enable sparse approximations of the forward computations. Given that the forward solutions are repeatedly, if not extensively, utilised during the image reconstruction process, considerable computational savings can be recorded whilst maintaining O(N) forward problem complexity. We verify with numerical results that, in practice, less than 5% of the involved coefficients are actually required for computations and, hence, needs to be stored. We finalise this work by addressing the impact to the inverse problem. It is worth underlining that the proposed scheme is independent of the actual family of wavelet basis functions of compact support.

Original languageBritish English
Title of host publication33rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS 2011
Pages3892-3896
Number of pages5
DOIs
StatePublished - 2011
Event33rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS 2011 - Boston, MA, United States
Duration: 30 Aug 20113 Sep 2011

Publication series

NameProceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS
ISSN (Print)1557-170X

Conference

Conference33rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS 2011
Country/TerritoryUnited States
CityBoston, MA
Period30/08/113/09/11

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