  Estimating the values of unknown parameters from corrupted measured data
faces a lot of challenges in ill-posed problems. In such problems, many
fundamental estimation methods fail to provide a meaningful stabilized
solution. In this work, we propose a new regularization approach and a new
regularization parameter selection approach for linear least-squares discrete
ill-posed problems. The proposed approach is based on enhancing the
singular-value structure of the ill-posed model matrix to acquire a better
solution. Unlike many other regularization algorithms that seek to minimize the
estimated data error, the proposed approach is developed to minimize the
mean-squared error of the estimator which is the objective in many typical
estimation scenarios. The performance of the proposed approach is demonstrated
by applying it to a large set of real-world discrete ill-posed problems.
Simulation results demonstrate that the proposed approach outperforms a set of
benchmark regularization methods in most cases. In addition, the approach also
enjoys the lowest runtime and offers the highest level of robustness amongst
all the tested benchmark regularization methods.
