The Regularization Method Of The Ultrasound Tomography

Ultrasonic tomography is a kind of technique which uses the scattering wave data received outside the media and realizes the inversion of the internal structure of the medium according to certain physical and mathematical relations.This paper used the fluctuations theory of ultrasound transmission in a continuous medium to deduce the forward scattering equation and inverse scattering field equation when ultrasonic waves past through the measured medium,and then inverted the internal structure of the object.Iterative algorithm and regularization method were adopted separately to solve the nonlinear problem of inverse scattering equation and the problem of the inverse scattering equation in the iterative process.The first kind of method is direct regularization.It is suitable for solving the small and medium linear discrete inapplicable system.Such methods are usually solved by matrix decomposition,among which the most commonly used one is singular value decomposition(SVD)because of its simple decomposition process and the stable numerical values.TSVD and TTLS are popular regularization methods based on SVD,which discard the small singular values in the coefficient matrix and keep a reliable part in the process of solving problem.Compared with classical Tikhonov regularization method,these two methods do not require priori information and is able to select regularization parameter conveniently.In this paper,the TSVD regularization method and Tikhonov-Gaussian regularization method are combined to improve the TSVD regularization method.The main idea of the improved TSVD was introducing the truncation parameters to divide the coefficient matrix into larger singular values and smaller singular values reliable and unreliable parts,and then using the Tikhonov-Gaussian method to correct the unreliable parts.This not only suppressed the amplification of noise on the data side caused by the smaller singular value,but also avoid the reliable part of the model affecting by the amendment.The second one is an iterative regularization method,which can reduce the computational complexity and speed up the operation when dealing with ill-posed problems.For large-scale linear discrete ill-posed systems,such methods are good choices.CGLS and LSQR are two commonly used Krylov subspace methods.The CGLS method applies conjugate gradient to solve the original equation.While the LSQR method applies Lanczos double diagonalization to solve the original equation.Considering the semi-convergence characteristics of the CGLS method,the CGLS method is improved.By applying the appropriate correction factor to the residual vector,the residual residual is then balanced during the iteration in order to suppress noise diffusion in the residuals,and further overcame the semi-convergence of original CGLS method,which contributeed to better reconstruction result.The experimental simulation and results analysis showed:(1)In general,the iterative regularization method converged faster than direct regularization method,and the degree of fitting to the model was higher than that of direct regularization method.(2)TSVD,the improved TSVD and TTLS methods could realize the regularization of the inverse scattering problem.the improved TSVD method enabled to get the most realistic solution to the original problem,followed by TSVD method,and then TTLS method.(3)The CGLS method and LSQR method had similar numerical results.The LSQR method has less memory capacity,larger computational complexity,but better numerical stability than those of CGLS method.(4)The improved CGLS method overcame the semi-convergence without great increase in the amount of computation and storage,and was better than CGLS and LSQR methods in the numerical stability and data fitting degree.In summary,in the case of strong scattering,the above-mentioned regularization methods could realize the inversion reconstruction of the internal structure of measured object with the contrast ratio of 20%,and result in good simulation results.