Preconditioned Iterative Methods for Algebraic Systems from Multiplicative Half-Quadratic Regularization Image Restorations

@article{Bai2010PreconditionedIM,
  title={Preconditioned Iterative Methods for Algebraic Systems from Multiplicative Half-Quadratic Regularization Image Restorations},
  author={Zz Bai and Yu-Mei Huang and Michael K. Ng and X Yang},
  journal={Numerical Mathematics-theory Methods and Applications},
  year={2010},
  volume={3},
  pages={461-474}
}
  • Z. Bai, Yu-Mei Huang, X. Yang
  • Published 1 November 2010
  • Computer Science, Mathematics
  • Numerical Mathematics-theory Methods and Applications
Image restoration is often solved by minimizing an energy function consisting of a data-fidelity term and a regularization term. A regularized convex term can usually preserve the image edges well in the restored image. In this paper, we consider a class of convex and edge-preserving regularization functions, i.e., multiplicative half-quadratic regularizations, and we use the Newton method to solve the correspondingly reduced systems of nonlinear equations. At each Newton iterate, the… 
View via Publisher
math.hkbu.edu.hk
3 Citations
Methods Citations
1

Figures and Tables from this paper

3 Citations

A preconditioned conjugate gradient method for multiplicative half-quadratic image restoration
Conjugate gradient method preconditioned with modified block SSOR iteration for multiplicative half-quadratic image restoration
TLDR
Both theoretical and numerical results show that the modified block SSOR preconditioned PCG methods can greatly improve the computation efficiency when solving the multiplicative half-quadratic regularized image restoration problem.
Binary Level Set Methods for Dynamic Reservoir Characterization by Operator Splitting Scheme
TLDR
By transforming the constrained optimization problem in an unconstrained one, the saddle point problem can be solved by Uzawas algorithms with operator splitting scheme, which is based on the essence of binary level set method.

References

SHOWING 1-10 OF 15 REFERENCES
BLOCK-TRIANGULAR PRECONDITIONERS FOR SYSTEMS ARISING FROM EDGE-PRESERVING IMAGE RESTORATION
Signal and image restoration problems are often solved by minimizing a cost function consisting of an l(2) data-fidelity term and a regularization term. We consider a class of convex and…
Nonlinear image recovery with half-quadratic regularization
TLDR
This approach is based on an auxiliary array and an extended objective function in which the original variables appear quadratically and the auxiliary variables are decoupled, and yields the original function so that the original image estimate can be obtained by joint minimization.
Analysis of Half-Quadratic Minimization Methods for Signal and Image Recovery
TLDR
The goal of this paper is to provide a systematic analysis of the convergence rate achieved by the multiplicative and additive half-quadratic regularizations, and determine their upper bounds for their root-convergence factors.
Constrained Restoration and the Recovery of Discontinuities
TLDR
The authors examine prior smoothness constraints of a different form, which permit the recovery of discontinuities without introducing auxiliary variables for marking the location of jumps and suspending the constraints in their vicinity.
On Inexact Preconditioners for Nonsymmetric Matrices
TLDR
The spectral properties of the preconditioned matrices and the finite-step termination properties of Theoretical Krylov subspace iteration methods with an optimal or Galerkin property are described with respect to these preconditionsers.
Constraint Preconditioning for Indefinite Linear Systems
The problem of finding good preconditioners for the numerical solution of indefinite linear systems is considered. Special emphasis is put on preconditioners that have a 2 × 2 block structure and…
Construction and analysis of structured preconditioners for block two-by-two matrices
TLDR
For the large sparse block two-by-two real nonsingular matrices, a general framework of structured preconditioners is established through matrix transformation and matrix approximations that can lead to high-quality preconditionsing matrices for some typical matrices from the real-world applications.
Structured preconditioners for nonsingular matrices of block two-by-two structures
  • Z. Bai
  • Computer Science
    Math. Comput.
  • 2006
TLDR
For the large sparse block two-by-two real nonsingular matrices, a general framework of practical and efficient structured preconditioners is established through matrix transformation and matrix approximations that can lead to efficient and high-quality preconditionsing matrices for some typical matrices from the real-world applications.
A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations
Constraint Preconditioners for Symmetric Indefinite Matrices
TLDR
Numerical results show that, for a suitably chosen $(1,1)$ block-matrix, this constraint preconditioner outperforms the block-diagonal and theBlock-tridiagonal ones in iteration step and computing time when they are used to accelerate the GMRES method for solving these block two-by-two symmetric positive indefinite linear systems.
...
...