Abstract

The time-reversal 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 times, which is a crucial step towards practical applications of the time-reversal method. In this paper, we introduce the concept of kurtosis into the time-reversal process to reconstruct not only spatial locations but also excitation times of the sources. Our method paves the way for extension and applications of the time-reversal method to real-world problems such as identifying radiation sources of different times in various environments. Numerical examples are presented to demonstrate the effectiveness of the proposed concept and method.