The Study on Truncated Singular Value Decomposition Method in Ultrasound Inverse Scattering Image Reconstruction
超声逆散射图象重建问题中截断奇异值分解正则化方法研究

To process the nonlinear property of ultrasound inverse scattering image, one should alternately solves the well-posed forward scattering equations for an estimated total field and the ill-posed inverse scattering equations for the desired object property function. Forward scattering equations can be solved by common method while inverse scattering equations is ill-posed and should be regularized. For ill-posed inverse scattering equations, very little perturbation in data will cause great change in the solution. So the iterative procedure depends strongly on the precision of the solution of ill-posed inverse scattering equations. Previous work on the ill-posed inverse scattering equations commonly used Tikhonov regularization which by adding small filter factors to original least squares problem and can't filter noise efficiently. The method for choosing regular parameter is difficulty in Tikhonov regularization because the parameter is continuous. This paper adopts the truncated singular value decomposition (TSVD) method to solve the inverse scattering equations which can filter noise better than Tikhonov regularization. Since the regularization parameter is an integer in TSVD method, it can be revised by an appropriate method. Different 'images with different structure are simulated by truncated singular value decomposition method equipped with a revised parameter choosing strategy. Simulation results show that this method associated with a good approach for choosing regular parameter can efficiently filter noise, and hence the quality and reliability of the reconstruction image can be improved. At the same time, this method can decrease computations at the iterative procedure.