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Estimating the values of unknown parameters from corrupted measured datafaces a lot of challenges in ill-posed problems. In such problems, manyfundamental estimation methods fail to provide a meaningful stabilizedsolution. In this work, we propose a new regularization approach and a newregularization parameter selection approach for linear least-squares discreteill-posed problems. The proposed approach is based on enhancing thesingular-value structure of the ill-posed model matrix to acquire a bettersolution. Unlike many other regularization algorithms that seek to minimize theestimated data error, the proposed approach is developed to minimize themean-squared error of the estimator which is the objective in many typicalestimation scenarios. The performance of the proposed approach is demonstratedby applying it to a large set of real-world discrete ill-posed problems.Simulation results demonstrate that the proposed approach outperforms a set ofbenchmark regularization methods in most cases. In addition, the approach alsoenjoys the lowest runtime and offers the highest level of robustness amongstall the tested benchmark regularization methods.

Perturbation-Based Regularization for Signal Estimation in Linear Discrete Ill-posed Problems