Regularization algorithms have been investigated extensively to solve the ill-posed inverse problem of electrical tomography. Sparse regularization algorithms with sparsity constrains have become popular in recent years. The iterative shrinkage thresholding algorithms have been applied to deal with the sparse regularization due to their simplicity and low calculation cost. However, the performance of the reconstructed images varies with the thresholding parameter and initial parameters of the iterative thresholding algorithm, which are selected manually. Inspired by the iterative varied thresholding operator, a fast iterative updated thresholding algorithm is proposed for electrical resistance tomography (ERT) and further a new scheme for updating the thresholding parameter adaptively during the iteration process is designed. More penalty is implemented with a larger thresholding parameter when the sparsity is reduced, and less penalty is implemented with a smaller thresholding parameter when the sparsity is increased. In addition, a speedup step is exploited in order to accelerate the progress. This proposed method is verified quantitatively in numerical simulation as well as in experiment test on a practical ERT system. Moreover, the impacts of different initial parameters are discussed in detailed, the simulation results demonstrate that the proposed method is almost unaffected by different initial parameters. The advantage of this method is that a higher spatial resolution image with a faster solving speed can be reconstructed with less iterations. The results indicate that the quality of images reconstructed by this proposed method outperforms that of traditional methods whether in size or location of the inclusion. It also has a stronger ability in preserving edges and noise immunity. Furthermore, the proposed method can be applied to image reconstruction in other kinds of tomography.
Based on acousto-electric modulation, ultrasound modulated electrical resistance tomography (UMERT) is expected to provide high spatial resolution by extracting more information about the conductivity distribution from data enriched by coupling impedance measurements to localized mechanical vibrations. A difference sensitivity matrix constructed from reference and the measured field is proposed for UMERT. Firstly, the difference sensitivity matrix, related to conductivity information of the measured field, can suppress the adverse influences of soft-field effects on image reconstruction, which usually causes relatively large errors in traditional electrical resistance tomography (ERT) image reconstruction. Secondly, the differential form adopted by the proposed sensitivity matrix reduces the effect of the feature of the nonlinearity of the electric field on the distribution of the sensitivity matrix, which is reflected in sensitivity with a relatively low value in the central area whilst with a high value in the boundary area. Finally, the differential form can also reduce the influences of systematic errors on measurement data and thus, further improve the spatial resolution of reconstructed images. In addition, three current excitation patterns are discussed in order to obtain the best sensitivity of boundary voltage variations to conductivity changes. The proposed sensitivity matrix and the corresponding reconstructed image results are compared with that based on Geselowitz’s sensitivity theorem in ERT and one constructed from the measured field in UMERT. Both theory and simulation results verify the feasibility of the proposed difference sensitivity matrix. The reconstructed images demonstrate higher spatial resolution, especially for the detection of small objects. It also has a stronger ability in identifying the size of the objects and noise immunity.
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