Perturbation-based regularization for signal estimation in linear discrete ill-posed problems
نویسندگان
چکیده
منابع مشابه
Perturbation-Based Regularization for Signal Estimation in Linear Discrete Ill-posed Problems
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 leastsquares discrete ill-posed problems. The propo...
متن کاملFractional Tikhonov regularization for linear discrete ill- posed problems
Tikhonov regularization is one of the most popular methods for solving linear systems of equations or linear least-squares problems with a severely ill-conditioned matrix A. This method replaces the given problem by a penalized least-squares problem. The present paper discusses measuring the residual error (discrepancy) in Tikhonov regularization with a seminorm that uses a fractional power of ...
متن کاملFractional regularization matrices for linear discrete ill-posed problems
The numerical solution of linear discrete ill-posed problems typically requires regularization. Two of the most popular regularization methods are due to Tikhonov and Lavrentiev. These methods require the choice of a regularization matrix. Common choices include the identity matrix and finite difference approximations of a derivative operator. It is the purpose of the present paper to explore t...
متن کاملSquare regularization matrices for large linear discrete ill-posed problems
Large linear discrete ill-posed problems with contaminated data are often solved with the aid of Tikhonov regularization. Commonly used regularization matrices are finite difference approximations of a suitable derivative and are rectangular. This paper discusses the design of square regularization matrices that can be used in iterative methods based on the Arnoldi process for large-scale Tikho...
متن کاملFGMRES for linear discrete ill-posed problems
GMRES is one of the most popular iterative methods for the solution of large linear systems of equations. However, GMRES generally does not perform well when applied to the solution of linear systems of equations that arise from the discretization of linear ill-posed problems with error-contaminated data represented by the right-hand side. Such linear systems are commonly referred to as linear ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Signal Processing
سال: 2018
ISSN: 0165-1684
DOI: 10.1016/j.sigpro.2018.05.005