Electrical impedance tomography reconstruction through simulated annealing with total least square error as objective function

Abstract

The EIT reconstruction problem can be solved as an optimization problem where the divergence between a simulated impedance domain and the observed one is minimized. This optimization problem can be solved by a combination of Simulated Annealing (SA) for optimization and Finite Element Method (FEM) for simulation of the impedance domain. This combination has usually a very high computational cost, since SA requires an elevated number of objective function evaluations and those, obtained through FEM, are often expansive enough to make the whole process inviable. In here it is presented a new approach for EIT image reconstructions using SA and partial evaluations of objective functions based on overdetermined linear systems. This new reconstruction approach is evaluated with experimental data and compared with previous approaches.

A review of electrical impedance tomography in lung applications: Theory and algorithms for absolute images

“…Martins and Tsuzuki [67], Martins et al [19] proposed an alternative EIT MAP reconstruction model that uses this property. The idea is to invert the consideration of a perfect FEM and errors in measurements.…”

“…Expression (39) has the quadratic form u T f(A)u, where u = j i q is a vector, A = K T K is a positive definite matrix and f(x) = x −1 is an analytic function, and it can be efficiently obtained using a connection between the Lanczos Algorithm (LA) and the Gaussian Quadrature (GQ). Martins and Tsuzuki [67], Martins et al [19] adapted the "Lanczos Bidiagonalization II" to exploit matrices such as A = K T K which are already in the decomposition form to evaluate (39). This is why this algorithm is here called herein SA-LB.…”

“…This leads to the idea of performing a two-step reconstruction: start the reconstruction process using the SA-CG technique, then switch to the SA-LB technique while keeping the optimization variable state. If both objective functions have approximately the same convergence trajectory, this should allow a cheaper reconstruction method than both approaches: SA-CG [18,61,62] and SA-LB [67,19]. A possible combination of the methods was proposed by Martins and Tsuzuki [70].…”

Reconstrução de Imagens de TIE usando Simulated Annealing, Evolução Diferencial e Algoritmos Genéticos

“…O que ocorre em cada iteração do SA adaptado para reconstrução de TIE está esquematizado a seguir [17], [20]: Algoritmo SA procedimento SimulatedAnnealing 1) // Solução inicial; // Temperatura inicial; // parâmetro de processo; // constante aleatória [0,1]; // número máximo de iterações antes da queda da temperatura T;…”

Reconstrução de Imagens de Tomogrfia por Impedância Elétrica baseada em Redes Neurais Convolucionais

“…TIE sobre outros métodos não invasivos estão os fatos de que ela não depende da emissão de radiação e de que o equipamento utilizado pode ser pequeno e portátil, com custo relativamente baixo. A TIE tem sido usada para monitoramento em tempo real de processos industriais e de análise biomédica (Martins and Tsuzuki, 2012;Silva et al, 2017).…”