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Electrical impedance tomography algorithm using simulated annealing search method
... First and second order optimization methods cannot be easily applied to this problem though, since the underlying objective function, calculated from the results of a computer simulation, is subject to numerical errors that are amplified on its derivatives. For that reason, some authors are turning towards zero order methods that require no gradient, and in particular, metaheuristics such as Simulated Annealing [8,13]. The downside of this approach is that it requires many more objective function evaluations, and, as it will be shown in section 3, those can be quite costly. ...
... Indeed, if i and j are two vertexes that do not share a triangle, K (σ) ij = 0. By equation (8), one can see that even if i and j are edges of the same triangle, it is possible to have K (σ) ij = 0, but this is a particular case, uncommon on irregular meshes and can be ignored here without loss of generality. As such, if one would look at the mesh of figure 1 as a graph, the matrix K would have the same zero/nonzero structure than its adjacency matrix. ...
... As seen in section 2.1, the EIT inverse problem can be formulated as an optimization problem, and as such, can be approached with SA. Indeed, in [8] Herrera et al. applied SA to the minimization of objective function (1) and by doing so managed to reconstruct very accurate conductivity distributions of the body, but at a very high computational cost. This is unsurprising, as each step of the SA involves the solution of a full FEM problem in order to evaluate the objective function. ...
... Therefore, we applied SA to solve the optimization problem, once the gradient of the objective function is not employed. Herrera et al. [19] developed a SA-based method to minimize the objective function using real subjects. They performed an accurate reconstruction of the conductivity distribution within the patient's body. ...
... Hence, a parallel SA applied to the EIT inverse problem is proposed here to reduce the convergence time. The strategy used by Herrera et al. [19] may not be the best to deal with variables with different sensitivities [2]. Therefore, the adaptive neighborhood SA [20] is adopted. ...
Electrical impedance tomography (EIT) is a portable low-cost medical image technique with fast time response characteristics. EIT can be approached as an optimization problem whose objective is to minimize the difference between the simulated and measured distributions. A preconditioned conjugated gradient is employed to solve a linear system with a symmetric sparse positive definite matrix. In order to increase its efficiency, a matrix format, the colored padded jagged diagonals storage (pJDS) format, is proposed. Parallelization is applied to several steps of the algorithm and at each step performance is observed to be superior to fast serial implementation. However, API overhead degraded the performance of the forward problem. Kernel consolidation combined with the pJDS format obtained a significant performance improvement. The inverse problem is solved as an optimization problem using the simulated annealing with adaptive neighborhood. While several instances of the conjugated gradients run on the GPU, the remaining processes are executed in parallel in the CPU. The GPU saturates at a speedup of 5 times as compared to CPU processing.
... between the measured electric potentials Φ i m and the calculated potentials Φ i c (σ ) for every applied current pattern. Indeed, the minimization of (4) is a classic approach to EIT [5,6,7,8]. In [5] it was pointed that the minimization of (4) using gradient-based algorithms is difficult, since (4) is often ill-conditioned. ...
... In [5] it was pointed that the minimization of (4) using gradient-based algorithms is difficult, since (4) is often ill-conditioned. Herrera et al. [6] avoided the computation of objective function gradients by means of SA and by doing so, managed to reconstruct very accurate conductivity distributions of the body, but at a very high computational cost. This is unsurprising, as each step of the SA involves the solution of a full FEM problem in order to evaluate the objective function. ...
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.
... O Annealing é o processo de resfriamento lento e gradual de um sólido até o estado de menor energia. Se o resfriamento não for gradual, o material fica preso em um estado de "menor energia local", com a estrutura atômica irregular e fraca [5]. Assim, o Simulated Annealing é uma metaheurística de otimização por busca local de escalada do monte, que pode pular mínimos locais. ...
A Tomografia por Impedância Elétrica (TIE) é um método de diagnóstico por imagem não-invasivo, não-destrutivo, de baixo custo e portátil que possui diversas aplicações hoje em dia. Tal método baseia-se na aplicação de uma corrente alternada de alta frequência e baixa amplitude em eletrodos posicionados, equidistantes, ao redor da superfície do domínio em análise, visando a reconstrução do mapa de condutividade ou resistividade elétrica de seu interior. A reconstrução das imagens de TIE, entretanto, não é algo trivial, pois trata-se de um problema inverso, mal-posto, governado pela Equação de Poisson. Neste trabalho apresentam-se algoritmos para a reconstrução de TIE baseados no algoritmo de Evolução Diferencial (ED), fazendo um comparativo deste com os métodos de Simulated Annealing (SA) e Evolução Diferencial com Simulated Annealing (EDSA) para análises qualitativas e quantitativas.
... As seen in section 2.3, the EIT inverse problem can be formulated as an optimization problem, and as such, can be approached with SA. Herrera et al. (2007) minimized objective function (4) with SA and by doing so, managed to reconstruct very accurate conductivity distributions of the body, but at a very high computational cost. This is unsurprising, as each step of the SA involves the solution of a full FEM problem in order to evaluate the objective function. ...
Electrical Impedance Tomography (EIT) is a imaging technique that attempts to reconstruct the impedance distribution inside an object from electrical currents and potentials measured at its surface. The EIT reconstruction problem can be approached as an optimization problem where one tries to maximize the matching between a simulated impedance domain and the observed one. This optimization problem may be approached by Simulated Annealing (SA), but at a large computational cost due to the expensive evaluation process of the objective function. We propose here a variation of SA applied to EIT where the objective function is evaluated only partially, while ensuring upper boundaries on the deviation on the behavior of the modified SA.
... As seen in section 2.3, the EIT inverse problem can be formulated as an optimization problem, and as such, can be approached with SA. Herrera et al. (2007) minimized objective function (4) with SA and by doing so, managed to reconstruct very accurate conductivity distributions of the body, but at a very high computational cost. This is unsurprising, as each step of the SA involves the solution of a full FEM problem in order to evaluate the objective function. ...
Electrical Impedance Tomography (EIT) is a imaging technique that attempts to reconstruct the conductivity distribution inside an object from electrical currents and potentials measured at its surface. The EIT reconstruction problem can be approached as an optimization problem where one tries to maximize the matching between a simulated impedance domain and the observed one. This optimization problem may be approached by Simulated Annealing (SA), but at a large computational cost due to the expensive evaluation process of the objective function. We propose here a variation of SA applied to EIT where the objective function is evaluated only partially, while ensuring upper boundaries on the deviation on the behavior of the modified SA. Copyright c ⃝2011 IFAC.
O SABIO – Simpósio de Inovação em Engenharia Biomédica, Tecnologias Aplicadas
à Saúde – foi realizado nos dias 07, 08 e 09 de junho de 2017 no Campus Recife da
Universidade Federal de Pernambuco – UFPE. Este evento é uma iniciativa de alunos
de graduação com parceria e apoio de professores do Departamento de Engenharia
Biomédica/UFPE e do Grupo de Pesquisa SABER Tecnologias Educacionais e Sociais.
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