A fast sparse reconstruction algorithm for electrical tomography

Abstract

Electrical tomography (ET) has been widely investigated due to its advantages of being non-radiative, low-cost and high-speed. However, the image reconstruction of ET is a nonlinear and ill-posed inverse problem and the imaging results are easily affected by measurement noise. A sparse reconstruction algorithm based on L1 regularization is robust to noise and consequently provides a high quality of reconstructed images. In this paper, a sparse reconstruction by separable approximation algorithm (SpaRSA) is extended to solve the ET inverse problem. The algorithm is competitive with the fastest state-of-the-art algorithms in solving the standard L2−L1 problem. However, it is computationally expensive when the dimension of the matrix is large. To further improve the calculation speed of solving inverse problems, a projection method based on the Krylov subspace is employed and combined with the SpaRSA algorithm. The proposed algorithm is tested with image reconstruction of electrical resistance tomography (ERT). Both simulation and experimental results demonstrate that the proposed method can reduce the computational time and improve the noise robustness for the image reconstruction.