The GPR Signal Reconstruction And Reverse Time Migration Based On The Project Onto Convex Set Algorithm

As a non-destructive,efficient,and highly visible geophysical method,Ground Penetrating Radar(GPR)is used in engineering inspection,geological disaster investigation,archaeology and other fields,and has became one of the important detection methods for fine detection of shallow geological structures.When electromagnetic waves propagate on shallow ground,they are susceptible to many factors such as complex underground media,road construction obstacles,undulating terrain,antenna coupling,and hardware performance.GPR signals collected in the field often appear incomplete,and direct signal processing and imaging will cause profiles the accuracy and resolution are reduced,and it is difficult to effectively identify the target body.The Project Onto Convex Set(POCS)algorithm is an important tool for reconstructing characteristic signals of underground media.It can effectively reconstruct the waveform information of irregular and large missing ratio signals such as frequency and amplitude.In view of its simple principle and high calculation accuracy,it has been widely used in the field of image and seismic data reconstruction.In order to achieve high-precision reconstruction of GPR signals,based on the POCS theory and Fourier sparse transformation conditions,this paper developed a missing GPR signal reconstruction algorithm,and successfully applied it to theoretical and measured GPR signal processing.In addition,it effectively combines reverse time migration imaging verifies the reconstruction quality of the POCS algorithm.The main research contents and conclusions are as follows:1)First,under the framework of compressed sensing theory,POCS is used to derive the time-domain iterative formula for the reconstruction of missing GPR signals under Fourier sparse transformation;secondly,in order to improve the reconstruction accuracy and efficiency,a window threshold is designed for efficient iterative update Fourier coefficients;Then,using Matlab programming software,a reconstruction program of missing GPR signals based on POCS was compiled.2)In order to test the correctness and effectiveness of the GPR signal reconstruction algorithm based on the loss of POCS in this article,the algorithm is applied to analog signals,and the Mean Absolute Error(MAE),Signal to Noise Ratio(SNR)and Peak Signal to Noise Ratio(PSNR)compare the reconstruction effects of the window threshold model,linear threshold model and exponential threshold model in POCS to verify the superiority of the window model;on this basis,the algorithm is applied to typical analog signals,through MAE,SNR quantitative analysis of the quality before and after reconstruction with PSNR indicators shows that the algorithm proposed in this paper can effectively restore the waveform information of the complete signal,and the reconstructed profile is very consistent with the complete profile;at the same time,it analyzes the ratio of missing signals and the number of iterations.The related factors that affect the POCS algorithm are analyzed.Finally,the POCS algorithm is applied to the reconstruction of the measured missing GPR signal,and the result accurately reconstructs the waveform characteristics of the underground target.3)The reconstructed GPR signal is subjected to reverse time migration imaging,and the reverse time migration results before and after reconstruction are compared and analyzed through the MAE,SNR and PSNR indicators,and it is shown that the reverse time migration imaging results of the reconstructed GPR signal have higher accuracy,better resolution,and can guide the subsequent data interpretation more effectively than the imaging results of the direct use of the missing signal.