Research On Fast And High Precision Reconstruction Methods Of Missing Gpr Signal Based On Projection Onto Convex Sets

Ground penetrating radar(GPR),as a high-frequency electromagnetic detection technology based on differences in electromagnetic properties,is widely used for fine detection of shallow geological structures such as underground cavities and collapses due to its advantages of simple operation,high detection accuracy,and non-destructive detection.The prerequisite for accurately obtaining the above-mentioned shallow structures using data processing and imaging methods is to collect high-quality GPR signals.However,due to factors such as obstacles and complex terrain at the collection site,the measured profile inevitably experiences sparse signal distribution and signal loss,which can easily result in the loss or damage of reflection and diffraction generated by underground targets.If the missing traces in the profile are zeroed,it is easy to generate artifacts in subsequent imaging,seriously reducing imaging accuracy and resolution.Therefore,it is particularly important to carry out interpolation reconstruction work for missing GPR signals.In addition,the field GPR data not only has missing signals,but also severe interference from random noise.The lack of signal affects the predictability of data,leading to a decrease in denoising performance.Missing signals will introduce noise during interpolation reconstruction,which can also make it difficult to accurately reconstruct.Therefore,on the basis of reconstruction work,it is necessary to study a simultaneous reconstruction and denoising method.Due to the fact that the projection onto convex sets(POCS)algorithm does not require prior information such as geological,geophysical,and geometric structures of the background medium,and has the advantages of simple principle,easy implementation,and high computational efficiency,it has been widely applied in the fields of image processing,seismic signal,gravity and magnetic signal reconstruction.Therefore,this article intends to conduct research on high-precision POCS reconstruction methods for missing GPR signals based on curvelet domain,efficient POCS reconstruction methods for missing GPR signals based on window threshold in frequency domain,and a POCS based method for simultaneous reconstruction and denoising of missing and noisy GPR signals.The main content and conclusions of this article are as follows:(1)The POCS algorithm,which is widely used in image processing,is combined with a curvelet wave transform with good sparsity characteristics.A high-precision reconstruction method for missing GPR signals based on the curvelet domain POCS algorithm is proposed.The reconstruction experiments of simulated and measured missing GPR signals show that compared with traditional linear and exponential threshold frequency domain POCS algorithms and linear threshold curvelet domain POCS algorithms,exponential threshold curvelet domain POCS reconstruction algorithms have higher reconstruction accuracy,lower mean absolute error,and higher signal-to-noise ratio and peak signal-to-noise ratio.The reconstruction results can provide high-quality GPR signals for subsequent processing and interpretation.(2)A window threshold model suitable for POCS reconstruction is proposed by introducing a rectangular filtering window as a threshold value and converting the numerical threshold value into a regional threshold value.An efficient reconstruction method for missing GPR signals based on window threshold POCS algorithm is constructed.Simulation and field experiments show that the window threshold model based on frequency domain POCS reconstruction method has higher accuracy for continuous missing signals than linear and exponential threshold models based on frequency domain POCS reconstruction methods.Compared with the curvelet domain POCS reconstruction method,the frequency domain POCS method based on the window threshold model can ensure the reconstruction accuracy while saving about 95% of the calculation time.Significantly improves computational efficiency.(3)A simultaneous reconstruction and denoising IWPOCS method for missing and noisy GPR signals was constructed by combining the POCS method that changes the algorithm order(IPOCS)with the POCS algorithm that adds weight coefficients(WPOCS).The experimental results show that compared to the original reconstruction only POCS method,IPOCS method and WPOCS method,IWPOCS has better reconstruction efficiency and denoising effect.The final results can provide high signal-to-noise ratio GPR signals for subsequent imaging and interpretation.