Sampling of finite elements for sparse recovery in large scale 3D electrical impedance tomography

Abstract

This study proposes a method to improve performance of sparse recovery inverse solvers in 3D electrical impedance tomography (3D EIT), especially when the volume under study contains small-sized inclusions, e.g. 3D imaging of breast tumours. Initially, a quadratic regularized inverse solver is applied in a fast manner with a stopping threshold much greater than the optimum. Based on assuming a fixed level of sparsity for the conductivity field, finite elements are then sampled via applying a compressive sensing (CS) algorithm to the rough blurred estimation previously made by the quadratic solver. Finally, a sparse inverse solver is applied solely to the sampled finite elements, with the solution to the CS as its initial guess. The results show the great potential of the proposed CS-based sparse recovery in improving accuracy of sparse solution to the large-size 3D EIT.

An accelerated version of alternating direction method of multipliers for TV minimization in EIT

“…Another shortcoming is the multiplier  which must go to infinity by the progression of the algorithm in order to guarantee that the solution of Eq. (21) converges to that of Eq. (13).…”

“…In many cases, a sequence of expansion coefficients of the signal over an orthonormal basis includes only a small number of nonzero entries, and is thus assumed sparse [11,17]. In many applications in EIT, the object under study involves an uninteresting background plus a number of interesting inclusions, which represents sparsity [11,[18][19][20][21].…”

“…In contrast with a great deal of sparsity regularization schemes that have been applied to EIT [16][17][18][19][20][21], the recent advances on TV minimization have not been paid due attention. As far as we know, TVAL3 is the most powerful TV algorithm in the context of image restoration [51][52].…”

A fast time-difference inverse solver for 3D EIT with application to lung imaging

“…However, according to our previous numerical results, the main drawback of the GPSR for application to 3D EIT is that its accuracy is severely deteriorated in determining very small inclusions [37]. This problem was addressed by adopting a compressive sensing scheme for sampling the finite elements covering the inclusions.…”

“…By application of a preprocessing PCG step, the proposed scheme improved accuracy at the cost of speed. For further information, the reader is referred to [37].…”