Time reversal imaging for sensor networks with optimal compensation in time.

Using extensive numerical simulations, several distributed sensor imaging algorithms for localized damage in a structure are analyzed. Given a configuration of ultrasonic transducers, a full response matrix for the healthy structure is assumed known. It is used as a basis for comparison with the response matrix that is recorded when there is damage. Numerical simulations are done with the wave equation in two dimensions. The healthy structure contains many scatterers. The aim is to image point-like defects with several regularly distributed sensors. Because of the complexity of the environment, the recorded traces have a lot of delay spread and travel time migration does not work so well. Instead, the traces are back propagated numerically assuming that there is some knowledge of the background. Since the time at which the back propagated field will focus on the defects is unknown, the Shannon entropy or the bounded variation norm of the image is computed and the time where it is minimal is picked. This imaging method performs well because it produces a tight image near the location of the defects at the time of refocusing. When there are several defects, the singular value decomposition of the response matrix is also carried out.