A reconstruction algorithm for electrical impedance tomography based on sparsity regularization

SUMMARY This paper develops a novel sparse reconstruction algorithm for the electrical impedance tomography problem of determining a conductivity parameter from boundary measurements. The sparsity of the ‘inhomogeneity’ with respect to a certain basis is a priori assumed. The proposed approach is motivated by a Tikhonov functional incorporating a sparsity‐promoting ℓ 1 ‐penalty term, and it allows us to obtain quantitative results when the assumption is valid. A novel iterative algorithm of soft shrinkage type was proposed. Numerical results for several two‐dimensional problems with both single and multiple convex and nonconvex inclusions were presented to illustrate the features of the proposed algorithm and were compared with one conventional approach based on smoothness regularization.