Reproducing Kernel-Based Best Interpolation Approximation for Improving Spatial Resolution in Electrical Tomography

Electric tomography (ET) is an advanced visualization technique with low-cost, rapid-response, nonradiative, and nonintrusive advantages compared with other tomography modalities. The imaging resolution of ET, however, is significantly low providing the required measurements that are far less than the number of pixels in a detection field. Presented here is a reproducing kernel-based best interpolation (RKBI) method that can greatly increase the number of numeric measurements in the ET process. For a group of available measurements, RKBI has the smallest approximation error compared to the existing interpolation methods. Furthermore, the error of RKBI can be easily estimated with no additional hardware and the need for actual measurements. The optimality of RKBI is validated using both theoretical and experimental frameworks, demonstrating that RKBI really improves the spatial resolution and steadiness of ET images.