Image Reconstruction Based on Fractional Tikhonov Framework for Planar Array Capacitance Sensor

Planar array capacitance sensor imaging is a nondestructive imaging technique that can provide the permittivity distribution of media across capacitance data measured by electrodes. However, the image reconstruction problem is ill-posed because the dimensions of sensitive field data and the capacitance data are substantially unmatched, which leads to unstable imaging and low imaging accuracy. This paper proposes an imaging methodology of the fractional Tikhonov framework with automatic parameter selection to visualize the permittivity distribution of the object field. The proposed methodology replaces the severely ill-posed inverse problem with a penalty least squares problem. The fractional power of the Moore-Penrose pseudoinverse is utilized as the weighting matrix to measure the residual error in regularization. A synchronous iterative automatic selection method is proposed instead of empirical selection to realize the automatic determination of fractional power and fractional regularization parameters. In addition, the residual error in the regularization process is reduced and the quality of the solution is improved. The numerical experiments indicated that the proposed algorithm can ensure the accuracy of the solution and can achieve high precision reconstruction images.