Article
Licensed
Unlicensed
Requires Authentication
On the role of sparsity in inverse problems
-
D. A. Lorenz
Published/Copyright:
February 4, 2009
Abstract
This paper addresses the regularization of linear inverse problems with so-called sparsity constraints in terms of ℓP-penalty terms. Error estimates and convergence rates are derived. The application of the generalized gradient projection method and the semismooth Newton method to the according minimization problem is shown. Numerical experiments show the efficiency of the semismooth Newton method.
Received: 2008-07-25
Published Online: 2009-02-04
Published in Print: 2009-February
© de Gruyter 2009
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- Minisymposium — Recent progress in regularization theory
- Recent results on the quasi-optimality principle
- An iterative thresholding-like algorithm for inverse problems with sparsity constraints in Banach space
- Regularization in Banach spaces — convergence rates by approximative source conditions
- On a parameter identification problem in linear elasticity
- Modified Landweber iterations in a multilevel algorithm applied to inverse problems in piezoelectricity
- On the role of sparsity in inverse problems
- Optimal convergence rates for Tikhonov regularization in Besov scales
- An overview on convergence rates for Tikhonov regularization methods for non-linear operators
- Modulus of continuity and conditional stability for linear regularization schemes
- Acceleration of the generalized Landweber method in Banach spaces via sequential subspace optimization
Articles in the same Issue
- Minisymposium — Recent progress in regularization theory
- Recent results on the quasi-optimality principle
- An iterative thresholding-like algorithm for inverse problems with sparsity constraints in Banach space
- Regularization in Banach spaces — convergence rates by approximative source conditions
- On a parameter identification problem in linear elasticity
- Modified Landweber iterations in a multilevel algorithm applied to inverse problems in piezoelectricity
- On the role of sparsity in inverse problems
- Optimal convergence rates for Tikhonov regularization in Besov scales
- An overview on convergence rates for Tikhonov regularization methods for non-linear operators
- Modulus of continuity and conditional stability for linear regularization schemes
- Acceleration of the generalized Landweber method in Banach spaces via sequential subspace optimization
