Name
Abstract | ||
|---|---|---|
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 and an error-contaminated data vector (right-hand side). This regularization method replaces the given problem by a penalized least-squares problem. It is well known that Tikhonov regularization in standard form may yield approximate solutions that are too smooth, i.e., the computed approximate solution may lack many details that the desired solution of the associated, but unavailable, error-free problem might possess. Fractional Tikhonov regularization methods have been introduced to remedy this shortcoming. However, the computed solution determined by fractional Tikhonov methods in standard form may display undesirable spurious oscillations. This paper proposes that fractional Tikhonov methods be equipped with a nonlinear penalty term, such as a TV-norm penalty term, to reduce unwanted oscillations. Numerical examples illustrate the benefits of this approach. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.cam.2017.04.017 | J. Computational Applied Mathematics |
Keywords | Field | DocType |
Inverse problems,Tikhonov regularization,Fractional Tikhonov,Nonlinear penalty | Tikhonov regularization,Mathematical optimization,Nonlinear system,Linear system,Matrix (mathematics),Mathematical analysis,Backus–Gilbert method,Regularization (mathematics),Inverse problem,Mathematics,Regularization perspectives on support vector machines | Journal |
Volume | Issue | ISSN |
324 | C | 0377-0427 |
Citations | PageRank | References |
1 | 0.35 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Serena Morigi | 1 | 142 | 20.57 |
| Lothar Reichel | 2 | 453 | 95.02 |
| Fiorella Sgallari | 3 | 217 | 22.22 |