Study On Algorithm For Cylindrical Reconstruction Based On Tikhonov Regularization

As an important type of inverse scattering problem,ultrasonic reconstruction algorithm based on diffraction tomography is widely applied in medical treatment,non-destructive testing,geological exploration and other fields.While,the traditional reconstructed method such as Born approximation method cannot solve non-linear and ill-posed problems well,and involve much more reconstruction errors.In these conditions,we present a new cylindrical reconstructed algorithm,which extends the original Born approximation theory and uses an iterative method to break the limit of the reconstructed frequency of Born approximation,the regularized method achieves well-posed calculation.In the form of numerical simulation,the algorithm is combined with some practical problems,and the some scatterers are reconstructed by new and conventional algorithms,and their results are compared with each other to verify the advantages of the new method.The main research contents of this thesis include the following aspects:1.Diffraction tomography is used to make three-dimensional scattered objects separated by different scattered layers.Thus method reduces the three reconstructed dimension to twodimension,and simplify the structure of the measured object.2.We extend the solving process by introducing an iterative method,through which,the scattering equation is divided into iterative equations.The iterative method is used to expand the frequency range of the reconstruction,so that the available reconstruction information is more accurate.3.The Tikhonov regularization is used to regularize the ill-posed equation solution in our algorithm,which makes the solution process more stable and achieves regularized,and avoids divergent results effeciently.Meanwhile,according to the characteristics of the scattering equation,the numerical simulation was used to verify the inverse scattering reconstruction algorithm.By comparing the results of Born approximation for the same scattering model,it is confirmed that the reconstruction algorithm can solve the inverse scattering problem effectively.In short,we have analyzed and solved the inverse scattering problem whose incident wave is ultrasound,from the theoretic analysis and numerical simulation,and we also present a diffraction reconstruction algorithm that can be applied in more complicated environments.Because the scattering equation we used also satisfies the electromagnetic wave,the method is applicable to other wave fields too,such as light waves and terahertz waves.