Research On The Imaging Method Based On Time-reversal

Time reversal(TR)technique is a kind of reverse operation in time domain.The radiated signals or scattered signals recorded by each element of a receiving array are time-reversed and then reradiated back into the original medium,i.e.,in a first-in last-out fashion.These reradiated-back signals will automatically focus at the locations of the original radiating sources or scattering sources.The automatic focusing property makes the TR technique to be attractive to applications in radar target detection,communication and medicine areas.This dissertation is concerned with the application of the TR technique in the imaging area.Based on analysis and comparision of sevseral popular TR imaging methods,a new TR imaging method,called “time reversal imaging based on synchronism”(shortly called TRIS),is proposed.The coventional TR imaging methods show a snapshot of the amplitude values of the time-reversed reradiated-back signals from the time-reversal mirror(TRM)at a specified instant(focusing instant).The present approach gives the image based on the fact that the reradiated-back signals from individual elements of TRM achieve their maximum values synchronously at target positions but non-synchronously at non-target positions.That is,a target is located based on whether the reradiated-back signals achieve their maximum values at the same instant at the point.From different viewpoints in producing the images,TRIS has some advantages over the existing TR imaging methods,including:(1)The computation of TRIS is completed in time domain,so for operation of ultrawideband,the computing burden of TRIS is much lower than those time-reversal imaging methods that are processed in frequency domain.(2)TRIS needs not consider the propagation from the transmitter to the imaging domain,so it makes the passive detection more practical.(3)For active detection,TRIS can locate multiple targets with only one transmitter,which considerably reduces the requirment of measured data and makes the method simpler.(4)On the imaging performance,TRIS has the excellent resolutions.It can solve the far-near or strong-weak prolem and overcome the issue of failing to locate the extended dielectric target resulting from the difficulty in finding the accurate focusing instant in the traditional time-reversal imaging methods.However,as the number of detecting targets increases,the settings of TRIS should be changing accordingly,i.e.,increasing the number of elements in each sub-array and decreasing the number of sub-arrays,which may result in resolution degration.To solve this issue,an improved TRIS scheme is proposed by combining the singular-value decomposition(SVD)of the frequency-frequency multistatic data matrix(FF-MDM)characterizing the transmission functions of the imaging system with TRIS,by which the multiple-target detection can be approximately decomposed into the multiple single-target detections using the TRIS.The work of this dissertation is composed of the following three parts.1.First,an introduction to the research-background and development of the TR technique,especially the progress of TR technique in the imaging area,is given.Then,the theory of the TR technique is formulated in detail.Finally,through analyzing and comparing,the merits and drawbacks of several currently popular TR imaging methods are concluded and illustarted with numerical examples.This part constitutes the base for us to propose the new TR imaging schemes.2.A new TR imaging method named “time reversal imaging based on synchronism(TRIS)” is proposed.First,the synchronism of the reradiated-back signals at the locations of the original radiating sources or scattering sources in case of two-dimensional(2D)scalar field is deduced,and the operating steps of the 2D TR imaging method based on the synchronism are described.Validation and advantages of the new approach for 2D targets are illustrated with several numerical examples.Next,the synchronism of the reradiated-back signals at locations of the original radiating sources or scattering sources in case of three-dimensional(3D)vector field is proved.Several numerical examples are provided to examine the imaging performance for one point-like target,two point-like targets at different distances,two extended targets with different scattering properties,and two point-like targets in inhomogeneous media.The advantages of the proposed TRIS method over the traditional time-reversal imaging methods are illustrated.3.As the number of the detected targets in imaging domain increases,the number of the elements in each sub-array should increase accordingly,so that the number of the sub-arrays would decrease.This would result in the degration of imaging resolutions.To solve this issue,an improved TRIS,called FF-MDM-TRIS,is proposed by combining the singular-value decomposition(SVD)of the frequency-frequency multistatic data matrix(FF-MDM)that characterizes the transmission functions of the imaging system with the TRIS.The FF-MDM is obtained by sampling the recorded signals by each element of TRM in frequency domain,and then the singular vectors encoding the radiated or scattered signal from a single target are retrieved by the operation of SVD of the FF-MDM.The singualar vectors are then used as the retransmitted signals in the TRIS method.Similar to the case of the single-target detection,FF-MDM-TRIS makes the number of sub-arrays to be the maximum(equal to the total number of the elements of TRM),so that the imaging results have high resolutions.In addition,FF-MDM-TRIS allows seletive imaging for any individual target.