2016/11/29 by Mohamed Suliman, Suliman, Mohamed, Tarig Ballal +3
Computer Science · Engineering · Mathematics · #Advanced Measurement and Metrology Techniques #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Optical measurement and interference techniques #Optimization and Control (math.OC) #Photoacoustic and Ultrasonic Imaging #cs.IT #math.IT #math.OC
paper · pdf · doi:10.48550/arxiv.1611.09742
13 pages, Journal
openalex publication_date 2016/11/29 · arxiv created 2017/01/10 · arxiv updated 2017/01/11 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28
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.