Electromagnetic time-reversal (TR) has been proven to be an effective and efficient method for solving source reconstruction problems. Different algorithms are proposed to deal with difficulties in real-world scenarios. In our previous work, we proposed the electromagnetic kurtosis methods and discussed the resolution in band-limited TR. However, traditional kurtosis methods may not work effectively with narrow bandwidth. This work further extends the idea of arbitrary-order kurtosis and demonstrates its capabilities of achieving super-resolution in real applications. Compared to other super-resolution techniques, the proposed methods are algorithmic simple and do not incorporate subwavelength structures. Numerical experiments show the field concentration beyond the diffraction limit which can increase the accuracy of source reconstruction with band-limited TR. Quantitative analysis is also presented to illustrate the characteristics of arbitrary-order kurtosis and its applications in multiple sources reconstruction or future complex environments.

Time-reversal (TR) is an effective method of solving inverse problems. However, the theory about the TR is still not clear. This work starts by examining fundamental laws in wave physics and electromagnetics and presents a revisit of the electromagnetic TR method. Then a cavity is employed, and the hardware experiments are performed to validate the TR as a robust and straightforward method for source reconstruction. Since the testing equipment has a limited working bandwidth, special algorithms are developed to transform the band-limited testing data into causal time-domain signals for the TR operations. The results verify the effectiveness of the TR method in real-world situations. The work presented in this paper paves the way for extensions and applications of the TR method toward solving complex, realistic problems.

In our previous study, a concept of electromagnetic kurtosis for time-reversal source reconstruction was presented. From a two-step process, the electromagnetic kurtosis can first identify the excitation time instants then localize the sources locations with time-reversal technique. In this paper, we extend the concept of the electromagnetic kurtosis from two different perspectives. The proposed space kurtosis and time kurtosis in the electromagnetic time-reversal process can directly reconstruct excitation time instants and spatial locations of sources respectively. The newly proposed time kurtosis takes the advantages of time-domain computational electromagnetics methods. Its algorithm with the threshold technique simplifies the procedures of multiple sources localization. Numerical experiments are conducted to verify the effectiveness of the presented algorithm.

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.