Study Of The Time Reversal Imaging Algorithm And Its Application Based On Space-frequency Decomposition

Time Reversal(TR)is a self-adaptive technique for spatial and temporal focusing,which has robust viability in any complex electromagnetic environment.The time compression,matched filtering and super resolution are its main characteristics.In recent years,this technique has been successfully applied to target detection,underwater communication,non-destructive testing,earthquake prediction,and so on.It’s worth mentioning that the TR imaging has become a hot research in the field of electromagnetic wave.This paper is mainly focused on the TR imaging algorithm based on the subspace decomposition.After the TR imaging algorithms using space-space decomposition have been studied,several novel TR imaging algorithms based on the space-frequency decomposition have then been proposed in the paper.All these new algorithms will further remedy the limitation of the present TR imaging theory system,increase the TR imaging efficiency,improve the TR imaging performance,enhance the TR imaging accuracy,and provide theoretical basis for the practical application of the TR imaging technique.First in this paper,the theoretical basis of the TR imaging technique is detailedly discussed.Both the vector and scalar wave equations are deduced,the solutions of which are explained with TR method.The reciprocity principle is discussed and used to explain the process of the TR technique.Together with the dyadic green function,the time reversal cavity is applied to prove and illustrate the spatial and temporal focusing characteristic of the time reversed vector electric field.Similarly,the time reversal cavity combined with the green function is applied to prove and illustrate the spatial and temporal focusing characteristic of the time reversed scalar field.The subspace theory is also introduced in the paper.All these works play a fundamental role for the later work based on the TR imaging technique.Secondly,this dissertation has studied TR imaging technique based on space-space decomposition of TR operator.The time-domain TD-DORT algorithm based on the space-space decomposition is studied in the paper.In contranst to the results given by frequency domain mode,both the range and cross-range resolutions given by the TD-DORT algorithm are better than those from the frequency-domain MF-DORT.Furthermore,the capabilities resisting the noise interference for the methods based on the DORT and TR-MUSIC have also been studied in the paper.And then,the TR imaging algorithm based on the space-frequency decomposition is proposed.After the limitations of the TR imaging methods based on the spapce-space decomposition are stated briefly,the space-frequency multistatic matrix is obtained using one measured scattered data.The singular value decomposition(SVD)is applied to the space-frequency matrix to acquire the left unitary matrix,the vectors of which are classified into the signal-subspace vectors corresponding to the targets and the noise-subspace ones.The signal-subspace vectors are utilized by the SF-DORT method to image the targtets,and both the signal and noise subspace vectors are utilized by the SF-MUSIC method to focus the targets.The accumulated values of the phase differences of all the vectors in the left unitary matrix are employed to determine the number of the targets in the probed domain.In order to improve the imaging accuracy,FD-SF-DORT and FD-SF-MUSIC methods are proposed in the paper,which are based on the full data measured by the TR array and will be self-averaging and statistically stable.The validities of all these methods have been demonstrated by the numerical simulation results.The images obtained by the FD-SF-DORT and FD-SF-MUSIC methods are much closer to the target locations than the SF-DORT and SF-MUSIC methods for their statistical stabilities.That is,the FD-SF-DORT and FD-SF-MUSIC methods have better capability resisting the noise interference than the SF-DORT and SF-MUSIC methods.At last,the TR imaging algorithms based on the space-frequency decomposition are applied to the dispersive and conductive(DPC)and random media,respectively.Lorentz model is utilized to simulate the DPC medium.The inverse filters are constructed to compensate the attenuation produced by DPC medium.The TR imaging algorithms based on the space-frequency decomposition are firstly applied to image the subsurface targets,and then applied to focus a single target or multi-targets embedded in the random medium.The spatially fluctuating permittivity of the random medium makes the phase shifts of the left singular vectors from space-frequency decomposition have a significant difference from those theoretical values,and this makes the focused images deviate from the real target locations.However,the FD-SF-DORT and FD-SF-MUSIC methods based on the full measured data will make the images close to the target locations for their statistical stabilities,which improve the imaging performance.In order to focus accurately on the weak targets which have weak scattering strength,the imaging methods based on the time reversal adaptive interference cancellation(TRAIC)technique are proposed.After the strong targets have been focused,they are treated as background scatterers.The weak target will relatively become strong one.It will improve imaging resolution of the weak targets,and enable us to obtain their images accurately.The spatial power-combining technique based on the space-frequency decomposition is also proposed in the paper.Once the frequency band of the retransmitted signal is increased,the combined power by the SF-DORT both in range and cross-range directions will become more concentrated and stronger than other mentioned methods.It must be emphasized that the TR imaging methods based on space-space decomposition need N measurements by the TR array,when the TR array has N antennas,to construct the space-space scattering matrix,in contrast to one measurement needed by the SF-DORT and SF-MUSIC methods to construct space-frequency scattering matrix.This greatly increases the imaging efficiency of the new algorithms,and makes them can focus the fast moving or active targets.