Research On Ultrasonic Tomography Method Based On Least Squares Method

Ultrasonic tomography technology is a non-invasive,low-cost and real-time nondestructive testing technology.Ultrasonic tomography is based on scattered wave data measured in the external environment of the target object,and relevant algorithms are applied to reconstruct the image of the internal characteristics of the object obtained through reverse calculation.There is an ill-posed relationship between the ultrasonic scattering wave and the unknown function of the internal characteristics of the object.In addition to the hardware conditions and detection methods of the system,the solution of the ill-posed problem directly affects the reconstruction quality of the ultrasonic imaging.Based on the theory of ultrasonic propagation,this paper establishes a mathematical model of ultrasonic testing environment,and uses approximation theory and least square method to simulate data fitting.However,the ill-posed nature of the ultrasonic tomography system and the instability of the least squares method limit the accuracy of the problem solving.In response to this issue,this article focuses on the relevant theories and reconstruction algorithms of ultrasound tomography.The main work includes:(1)The ultrasonic propagation characteristics and the form of wave equation are studied,the forward scattering mathematical model is established,and the scattering field and the whole field equation are discretized by the method of moments.The scattering model is solved by the Born approximation theory,and simulated by the regularization method.(2)The basic principle of the least squares method is systematically described,and the mathematical model and establishment process of the least squares method applied to image reconstruction are analyzed and discussed.In view of the shortcomings of the least squares method in image reconstruction,the feasibility of the method is proved by improving the stability of the least squares method.(3)The truncated complete least squares method is used to study the ill posed and unstable nature of the equation.Picard criterion is used as the condition for regularization processing of the discriminant reconstruction model,and the truncated parameters of the truncated total least squares method are properly selected to achieve regularization processing of the inverse scattering problem.The TTLS algorithm is improved by combining the TTLS algorithm with the Tikhonov Gaussian method.While using perturbation vectors and matrices to correct data item perturbations,the filtering factor from the Tikhonov Gaussian method is introduced on the basis of the moment method to correct smaller singular values,avoiding the impact of discarding smaller singular values on the solution.Through experimental verification,the improved TTLS algorithm greatly improves the ill posedness and instability of the equation,and greatly improves the imaging quality.(4)The iterative reweighted least squares method is used to study the ill-posed nature and instability of the equation.Aiming at the problems in the reconstruction process,the DWT algorithm and IRLS algorithm in compressed sensing theory are combined and applied to ultrasonic imaging.Using discrete wavelet transform to sparsely transform ultrasound data,sampling and measuring high and low frequency coefficients,and reconstructing measurement coefficients using iterative reweighted least squares.The weighting factor is updated according to the residual estimate of each iteration to obtain high-quality imaging.Through experimental comparison and verification,the DWT-IRLS algorithm has higher imaging quality and more obvious detail features,which can effectively improve the ill posed and unstable nature of the equation.Furthermore,the simulation run time of TTLS algorithm,the improved TTLS algorithm and DWT-IRLS algorithm are further analyzed.From the subjective and objective aspects,the DWT-IRLS algorithm reconstructed the original image with less sampled data,greatly reducing the run time while ensuring the imaging effect.