The motivation for ultrasound tomography is the location and identification of malignant human breast tissues for the purpose of detecting breast cancer. Although mammography is widely used for breast cancer detection, it has a high false positive rate and does not always accurately separate malignant tissue from benign tissue. Ultrasound tomography is used to compensate for these shortcomings. The computational model for ultrasound tomography is based upon solving an inverse scattering problem by finding the approximate total field and unknown scattering function using an iterative method. The principal computational problem involved is the solution of an ill-conditioned linear system, $Xy\approx b$, arising from an ill-posed problem written as an integral equation. In this paper, we explore the DSVD and the DGSVD regularization methods to solve the inverse scattering problem. The DGSVD algorithm gives better results than the DSVD algorithm when we introduce noise in either one or both sides of the linear system $Xy\approx b$.