Adaptive Group-Based Sparse Representation for Image Reconstruction in Electrical Capacitance Tomography

This article presents an adaptive group-based sparse representation scheme for image reconstruction in electrical capacitance tomography. Compared to conventional sparsity-based methods, the proposed method can accurately recover the shape and location of abnormities by exploiting local self-similarity and the sparsity of the image in the form of a group, consisting of a central block and neighboring local blocks. Each group can be represented by sparse coefficients and representation matrices obtained via adaptive self-learning from the current reconstructed image, leading to more sparsity and less computation. This scheme can be efficiently solved by the split Bregman iteration method, which can achieve accurate reconstruction within a few iterations. It has advantages in efficiently exploring the global sparsity and neighboring self-similarity in the reconstructed image simultaneously for enhanced image quality. Numerical simulations and phantom experiments were carried out to validate the proposed method. Results show that the proposed method can reconstruct more accurate images of abnormities of complex shapes than typical sparsity-based methods by consuming less computational resources. This is of great potential in fulfilling the high requirements on both the temporal and spatial resolutions in the imaging of dynamic processes, such as multiphase flows.