ECT image reconstruction based on alternating direction approximate newton algorithm

As a simple linearization of a highly nonlinear problem of image reconstruction in Electrical Capacitance Tomography (ECT), this approach suffers from drawbacks such as mismatches of position and size of the objects being imaged. To solve the ill-posed and nonlinear inverse problem of ECT image reconstruction, an alternating direction approximate Newton (ADAN) method is developed. The algorithm is based on the alternating direction method of multipliers (ADMM) and an approximation to Newton's method in which a term in Newton's Hessian is replaced by a Barzilai-Borwein (BB) approximation. The numerical experiments show that ADAN has the advantages of fast convergence speed and high imaging accuracy. Compared with the Landweber method, Newton's method and conjugate gradient algorithm, ADAN algorithm is a more stable process, image reconstruction quality is improved significantly. Especially for the cross model and sunrise model, compared with Newton iterative algorithm, image relative error reduced by 0.585 and 0.369, image correlation coefficient increased by 0.498 and 0.431.