Sparsity prior for electrical impedance tomography with partial data

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.

17 pages, 12 figures

References in corpus (3)

• Inverse Problem for a Curved Quantum Guide
• Monotonicity based shape reconstruction in electrical impedance tomography
• 3D Reconstruction for Partial Data Electrical Impedance Tomography Using a Sparsity Prior

Cited by in corpus (6)

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• Distinguishability revisited: depth dependent bounds on reconstruction quality in electrical impedance tomography
• Direct inversion from partial-boundary data in electrical impedance tomography
• Propagation and recovery of singularities in the inverse conductivity problem
• 3D Reconstruction for Partial Data Electrical Impedance Tomography Using a Sparsity Prior
• A shape optimization approach for electrical impedance tomography with point measurements