An Improved Sparse Reconstruction Algorithm Based on Singular Value Decomposition for Electrical Resistance Tomography

Abstract

Electrical Resistance Tomography (ERT) is a technique for reconstructing internal conductivity distribution of the measured field from the boundary data. Image reconstruction of ERT is a nonlinear and ill-posed inverse problem. Regularization method is used to solve inverse problem, and the sparse reconstruction by separable approximation algorithm (SpaRSA) is a relatively effective method. However, the reconstructed image quality of the method is easily affected by noise. In order to improve the noise immunity of sparse regularization algorithm, an improved sparse regularization algorithm is proposed in this paper. We transform the sensitivity matrix by singular value decomposition (SVD) and then modify the smaller singular values which may cause instabilities. Both simulation and experimental results show the effectiveness of the proposed method in improving the image quality with different noise intensities.