A fast iterative updated thresholding algorithm with sparsity constrains for electrical resistance tomography

Abstract

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.