3-D Image Reconstruction in Planar Array ECT by Combining Depth Estimation and Sparse Representation

In this article, a novel 3-D image reconstruction method was proposed for planar array ECT by combining depth estimation and sparse representation. The central depth of target in the region of interest is first estimated from an image initially reconstructed by the Tikhonov regularization. Second, sparse representation is employed to depict the permittivity distribution using the Gaussian radial basis functions defined at voxels over the plane in the estimated depth. Then, the 3-D image is reconstructed by solving a dedicated optimization problem using the Gauss–Newton method. The proposed method reduces the dimension of the unknowns, improves the condition number of the inverse problem, and enhances the image quality greatly. Numerical simulations and experiments were carried out to validate the proposed method. Results show that the proposed method can provide more accurate 3-D images of single or multiple inclusions at varying depths than conventional Tikhonov, total variation (TV), and Landweber methods while relieving the adverse effect of the nonuniform sensitivity of planar array ECT with varying depths on image reconstruction. The proposed method is of great potential in detecting and imaging subsurface abnormities.