Image Reconstruction of Electrical Capacitance Tomography Based on an Efficient Sparse Bayesian Learning Algorithm

Image reconstruction is the main research problem of electrical capacitance tomography (ECT). In this article, a novel ECT image reconstruction algorithm based on an efficient sparse Bayesian learning (ESBL) algorithm is presented. This algorithm takes the Gaussian-scale mixture model as the prior distribution of the parameters to increase the flexibility of the model. Then, a surrogate function is used to replace the Gaussian likelihood function to reduce the computational complexity of the algorithm. Finally, the original cost function is equivalently converted into a concave–convex optimization problem through logarithm, and the block coordinate descent (BCD) method is used to solve the problem under the majorization–minimization (MM) framework. In order to verify the effectiveness of this algorithm, the Laplace distribution and the Student’s T distribution are used as the prior distribution of the parameters to achieve two specific implementations of this algorithm, and simulation and experiments are carried out. Compared with the sparse Bayesian learning (SBL) algorithm, the Laplace prior-based Bayesian compress sensing (LPBCS) algorithm, the total variation (TV) algorithm, and the Landweber algorithm, the presented EBSL algorithm with the Laplace prior distribution has better image quality and fairly good real-time performance.