Time-Reversal Source Reconstruction With Electromagnetic Kurtosis

The time-reversal (TR) technique has been developed to solve inverse problems and to reconstruct sources. However, much work on the topic so far has not considered the determination of source excitation time instants, which is a crucial step toward practical applications of the TR method. In this article, we introduce the concept of kurtosis into the TR process to reconstruct not only spatial locations but also excitation time instants of the sources. Our method paves the way for extensions and applications of the TR method to real-world problems such as identifying radiation sources of different time in various environments. Numerical examples are presented to demonstrate the effectiveness of the proposed concept and method.