| Magnetic induction tomography(MIT) is a new method for mapping the electrical conductivity distribution of biological tissue according to electromagnetic detection principle. It has some unique advantages, such as noninvasive, non-contact, functional imaging, suitable for single detection and continuous monitoring, and it is a new research branch of electrical impedance tomography(EIT) technology.MIT algorithm is one of the key technology in MIT. Nowadays, all the proposed MIT algorithms, such as the back-projection algorithm and Newton iterative algorithm, use one single frame data for static imaging or two frame data for finite-difference imaging, which means that these algorithms ignore the correlation between the measured data. In some sense, this may cause some impact on the reconstruction result. According to the characteristics of MIT for continuous monitoring, this paper presents two kinds of new MIT algorithms which directly take correlations between successive measured data frames into account, which mainly includes the following two aspects:(1) The linear Kalman filter algorithmThe linear Kalman filter algorithm(LKF) is proposed in this paper which is based on the principle of the classical Kalman filter algorithm(KF), and programmed by C++ language. The reconstruction is finished in terms of an augmented measured data vector, which concatenate the conductivity distribution from the d frames previous and current moment frame. In order to evaluate the performance of the LKF algorithm, this paper sets all kinds of simulation models in the background of homogeneous conductivity distribution, using their MIT forward calculation results to replace the measured data, then reconstructing the conductivity distribution.This paper uses objective evaluation methods to evaluate the quality of reconstructed images, which includes reconstructed dimension error(RDE) and reconstructed position error(RPE).The results show that: 1) the positions of the disturbance targets in the reconstructed images are obviously tending to the edge of the images, but the ratio of the disturbance to the background conductivity is similar; 2) RDE is too large comparing to 1, and RPE is large, which means that the size and position of the perturbation target are slightly offset in the reconstructed images; 3) the conductivity changes curves of the one single disturbance target are drew in simulation models and reconstructed images, respectively. The correlation coefficient is 0.2778. The results show that the change trends of the two curves are consistent, but there is a big error. In a word, LKF algorithm has a poor performance in image reconstruction.(2) The temporal one-step Gauss-Newton algorithmThis paper proposes a new MIT algorithm—the temporal one-step Gauss-Newton algorithm(TGN), which directly takes correlations between successive measured data frames into account, based on the principle of the traditional one-step Gauss-Newton algorithm(GN). The image reconstruction is finished in terms of an augmented measured data vector, which concatenate the conductivity distribution from the d previous, current moment and d future frames.TGN algorithm mainly involves three parameters, which are regularization parameter, inter frame correlation coefficient and the number of measurement data frames.In order to select a suitable regularization parameter, the simulation model of a single disturbance target under different regularization parameters is reconstructed. The parameters of Tikhonov regularization method are 1e-002, 1e-003, 1e-004, 1e-005, 1e-006, 1e-007 and 1e-008. The results show that: 1) the reconstructed image completely divergence when the regularization parameter is 1e-007 or 1e-008; 2) RDE value is 1, and the RPE value is small, when the regularization parameter is 1e-004, 1e-005 or 1e-006. But the reconstructed artifact degree increased with the decrease of the regularization parameter; 3) The difference between RDE and 1 is increased, and the RPE value is increased when the regularization parameter is 1e-002 or1e-003, which means that the size of the perturbation target is larger, and the position is different. After consideration, the 1e-004 is chosen as the regularization parameter of following simulation experiment.In order to evaluate the impact of inter-frame correlation on reconstructed image, drawing the conductivity changes curves of the one single disturbance target in simulation models and reconstructed images, respectively, under the condition of different inter-frame correlation. And the correlation coefficient is 0.2901, 0.4983, 0.9999, respectively. The results show that with the increase of the inter-frame correlation, the error decreases, and the ability of the algorithm to track the conductivity change is also more and more accurate.In order to compare the impact of the number of measured data on reconstructed image, using 3 frames, 5 frames and 7 frame simulation data to reconstruct the conductivity distribution of simulation model which includes one single disturbance target, respectively. The results show that: 1) the visual effect of the reconstructed image is very high-quality, and the position of disturbance target is accurate and the size is equivalent, and the ratio of the disturbance to the background conductivity is similar; 2) The RDE value of the reconstructed image is 1, and the RPE value is small, which means that the size of disturbance target in the reconstructed image is equal and the position is accurate. Therefore, the following simulation experiments using 3 frames measured data for image reconstruction.In order to evaluate the performance of the TGN algorithm, this paper sets all kinds of simulation models in the background of homogeneous conductivity distribution. The forward calculation results are used to replace the measured data and reconstruct the conductivity distribution.The reconstructed images of some simulation models which include one single disturbance target, two disturbance targets, and three disturbance targets are high-quality, respectively. The position and size of disturbance target are accurate, and the ratio of the disturbance to the background conductivity is also similar. The RDE value of the reconstructed image is small, which means that the size of the disturbance targets in the reconstructed image is equal to the simulation models, and the RPE value is also small, which means that the position of the disturbance target in the reconstruction image is accurate. However, the position and size of disturbance targets are changed slightly, when reconstructing the images of some simulation models which include a large size disturbance target and the size and position of the disturbance target is gradually changing, respectively. And the RDE and RPE value of the reconstructed images are slightly larger, which means that the positioning ability of the algorithm is slightly decreased.In order to evaluate the ability to trace the changes of conductivity, the conductivity changes curves of the one single disturbance target in simulation models and reconstructed images are drew, respectively. The results show that the two curves are almost coincident, and the correlation coefficient is 0.9999, indicating that the algorithm can track the conductivity changes accurately.The 0.01%, 0.02%, 0.05%, 0.1%, 0.2%, 0.5%, 1%, 10%, 20% and 30% white Gaussian noise are added on simulation data, then reconstructing the images using these data. The results show that: 1) fixing regularization parameters, with the increase of the noise level, perturbation target size increases, and position offset slightly, until the reconstructed image divergence; 2) with the increase of the regularization parameter, the noise level that make the reconstructed image divergence is gradually increased, which indicates that a reasonable regularization parameter can improve the noise performance of the algorithm.In a word, the performance of the TGN algorithm is good, and it is an effective temporal MIT algorithm.In summary, this paper makes a research on the temporal MIT algorithm, which directly takes correlations between successive measured data frames into account, and two kinds of temporal MIT algorithm are derived. The performance of LKF algorithm is poor, and TGN algorithm shows a good imaging performance. It lays a good foundation for further study on temporal MIT algorithm, and provides a new choice for MIT continuous monitoring. |
