Time-Reversal Source Reconstruction With Electromagnetic Kurtosis

Source Reconstruction with the Electromagnetic Space Kurtosis and Time Kurtosis in the Time-Reversal Technique

“…In our previous work, the electromagnetic kurtosis was proposed to identify source excitation time intants [21]. As it is a measure of the space distribution of an electric (or magnetic) field at a specific time step n, we re-write it here and define the electromagnetic space kurtosis (hereinafter referred to as "space kurtosis") as follows:…”

“…Theoretically, at the time steps = − in the phase #2, the output signal of (6) [ − ] is larger than the fields at any other non-source locations, contributing to the field concentrations at the original Q source locations [21].…”

“…In our previous work, the space kurtosis of ( 1) was incorporated into the phase #2 of the TR process [21]. As described in Section II, the space kurtosis can determine the source(s) excitation time instant(s) by identifying the maximum (local maxima) value(s) of itself.…”

“…It is a scaled version of the ratio between the fourth central moment and the square of the second central moment. Inspired by these ideas, we introduced the electromagnetic kurtosis and incorporated it into the electromagnetic TR technique in our previous work [21].…”

Source Reconstruction with the Electromagnetic Space Kurtosis and Time Kurtosis in the Time-Reversal Technique

“…Theoretically, at the time steps 𝑛 = 𝑁 − 𝑛 𝑞 in the phase #2, the output signal of (6) 𝑠 𝑞 [𝑁−𝑛 𝑞 ] is larger than the fields at any other non-source locations, contributing to the field concentrations at the original Q source locations [21].…”