Image Reconstruction for Electrical Capacitance Tomography Through Redundant Sensitivity Matrix

Image reconstruction in electrical capacitance tomography usually employs sensitivity matrices that map the relation between permittivity distribution and sensor readings. As a simple linearization of a highly nonlinear problem, this approach suffers from drawbacks, such as mismatches of position and size of the objects being imaged. To overcome these issues, we propose a sparse reconstruction scheme that employs a redundant sensitivity matrix built with the K-singular value decomposition dictionary learning method and nonlinear simulation. This redundant sensitivity matrix is trained with real data and, thus, is able to better capture typical structures of the object under measurement. As the reconstruction has prior information that the solution is sparse, we solve the optimization with greedy algorithms to obtain a true <inline-formula> <tex-math notation="LaTeX">$\ell _{2}$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\ell _{0}$ </tex-math></inline-formula> solution. We show through simulations and real-world experiments that the proposed method improves reconstructed images quality even with reduced number of measurements.