Modified Tikhonov Regularization Method And Application In Radar Detection

Radar detection of objects is based on the propagation and scattering characteristics of electromagnetic waves in the medium.After the data is collected and inverted,the surface and internal information of the object can be obtained.Because this method has non-contact,non-destructive characteristics,it is widely used in various detection applications,such as geological exploration,water resources detection and environmental protection.The result and quality of radar data inversion directly affect the effect of radar detection.Therefore,it is important for radar detection to improve the result of inversion.However,due to the ill-posed problem of inversion,that is the instability of the ill-posed problem,the result of the inversion is often subjected to certain restrictions.The regularization is an effective method to solve the ill-posed problem of inversion.This dissertation introduces the related theories of inversion problems and regularization methods at first.The smaller singular values in the coefficient matrix lead to the ill-posedness of the inverse problem.In the analysis of the regularization method,it was found that the correction of the large singular value did not improve the ill-conditionedness,but introduced the deviation too much.Aiming at this problem,this dissertation proposes a regularization matrix correction method based on singular value ratio to enhance the correction of smaller singular values and reduce the correction of large singular values.After the singular value decomposition of the coefficient matrix,the threshold singular value is determined in the singular value matrix by the conditional number method.Calculate the square root of the ratio of the threshold singular value to the singular value,and construct a diagonal matrix of the square root.Combine the diagonal matrix with the left singular value vector matrix to construct a new matrix,which is the regularization matrix of the algorithm.In this dissertation,we selected three sets of numerical data for calculation.We compared the results of least squares,truncated singular value,ridge estimation and the algorithm of this paper.The comparison results show that the regularization matrix correction method proposed in this paper can improve the accuracy of the inversion results.In order to prove the effectiveness of the proposed method,the dissertation takes the ill-posedness in the borehole tomographic inversion of borehole radar as an example,and carries out the actual inversion calculation and analysis.In the travel time tomography of radar detection,the ray tracing algorithm is often used to simulate the process of electromagnetic wave propagation.In the process of mesh discretization of the detection area,each ray is divided into several segments,the matrix of detected data consisting of multiple rays is a sparse matrix,which leads to the ill-posed problem of time-lapse tomography.In this dissertation,we choose the direct ray tracing method to construct the coefficient matrix of traveltime tomography,and use the standard Tikhonov regularization method and the algorithm to invert the problem.