Autofocus Sparse Imaging For Through-the-wall Radar With Unknown Wall Parameters

Because of its strong penetration performance and high resolution,ultra-wideband(UWB)through the wall radar has been widely concerned and studied by the scientific and industrial circles,and plays an important role in the fields of public security,search and rescue,enemy reconnaissance and so on.In recent years,in the imaging of through-wall radar,due to the sparse characteristics of the target,a large number of sparse imaging methods are studied by introducing the compressed sensing theory.However,these methods have some problems such as high computational complexity,large memory and long imaging time.In addition,when the parameters of the wall are unknown,the existing sparse imaging method is difficult to achieve the correct positioning and clear imaging of the target.In view of the above problems,this paper makes the following research:1.Aiming at the problems of high computational complexity and large memory requirement of the existing sparse imaging,an efficient reconstruction method of TV-MAP sparse imaging based on MM optimization is proposed.In this method,firstly,the update formulas of the relevant parameters and sparse reflection coefficient in the TV-MAP sparse imaging method under MM optimization is given;then,by using the characteristics of the ultra-wideband narrow pulse waveform and the sampling characteristics of the impulse function,the related operation including the dictionary matrix in the alternative and iterative updating formula is replaced by linear convolution and hash table through the corresponding transformation of the transmitted signal sequence,It avoids the construction,storage and calculation of the dictionary matrix,thus effectively reduces the computational complexity and required memory.In addition,the influence mechanism of wall parameters on sparse imaging model is analyzed.Simulation results demonstrate the importance of the wall delay compensation and the effectiveness of the proposed efficient reconstruction method.2.Aiming at the problem of sparse imaging under unknown wall parameters,a autofocusing method combining the prediction of wall parameters and image aggregation is proposed.The method estimates the wall parameters in two stages.In the first stage,the preliminary estimated value of wall parameters are obtained by establishing the objective function,which includes the estimated time delay difference between the front and rear wall surface echo and the theoretical time delay difference.In the second stage,by selecting the candidate set of wall parameters in a small range near the preliminary estimated value of wall parameters obtained in the first stage,and using different wall parameters included in the candidate set for imaging used efficient TV-MAP sparse imaging based on MM optimization,the quality of imaging results is evaluated,and the corresponding wall parameters and images are output as the final estimated value of wall parameters and the final imaging results respectively when the evaluation is optimal.Compared with the traditional autofocusing search optimization method,this method reduces the range of candidate sets and imaging times.Finally,the simulation results show that this method can achieve the wall parameter estimation,eliminate the position offset,and get the clear image of the target behind the wall.3.In the existing autofocusing sparse imaging methods,which updates the sparse reflection coefficient and wall parameters alternately and iteratively,the existence of dictionary matrix will lead to the problem of long imaging operation time and large memory required.To solve this problem,an efficient autofocusing sparse imaging method without dictionary is proposed.First,the autofocusing sparse imaging model of the parameterized dictionary is given;then the TV-MAP efficient sparse reconstruction method based on MM optimization is used to update the sparse reflection coefficient.For the updating of the wall parameters,through the Taylor series expansion of the parametric dictionary,the updating formula of the wall parameter increment is obtained,and the related operation of the matrix included in the updating formula is replaced by linear convolution and hash table,so that in the whole process of autofocusing sparse imaging,the construction,storage and calculation of the dictionary matrix are avoided,and the operation time and memory required are reduced.At the same time,when the parameters of the wall are unknown,the position deviation of the target is well corrected,and the efficient autofocusing sparse imaging of the target behind the wall is realized.