Sparsity prior for electrical impedance tomography with partial data

TL;DR

This paper introduces a flexible sparsity-based regularization method for electrical impedance tomography with partial boundary data, significantly improving reconstruction quality by incorporating prior spatial information.

Contribution

It proposes a novel regularization framework using spatially distributed parameters and a generalized conditional gradient method for efficient partial data EIT reconstruction.

Findings

Enhanced reconstruction accuracy with prior information

Effective handling of partial boundary measurements

Comparison shows advantages over total variation methods

Abstract

This paper focuses on prior information for improved sparsity reconstruction in electrical impedance tomography with partial data, i.e. data measured only on subsets of the boundary. Sparsity is enforced using an $\ell_1$ norm of the basis coefficients as the penalty term in a Tikhonov functional, and prior information is incorporated by applying a spatially distributed regularization parameter. The resulting optimization problem allows great flexibility with respect to the choice of measurement boundaries and incorporation of prior knowledge. The problem is solved using a generalized conditional gradient method applying soft thresholding. Numerical examples show that the addition of prior information in the proposed algorithm gives vastly improved reconstructions even for the partial data problem. The method is in addition compared to a total variation approach.