An Improved Singular Value Modification Method for Ill-posed Problems

Based on the relationship between the Gaussian and Tikhonov filter functions, we choose the Gaussian filter function as the regularization matrix, and propose an improved singular values modification method for ill-posed problem, we term it the Tikhonov-Gaussian method. Simulation results from the downward continuation of the model gravity data show that the improved singular values modification method has significant quality advantages in comparison to the standard Tikhonov method.