Constrained Restoration and the Recovery of Discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Fast Algorithm for Deblurring Models with Neumann Boundary Conditions
SIAM Journal on Scientific Computing
On Inexact Preconditioners for Nonsymmetric Matrices
SIAM Journal on Scientific Computing
Analysis of Half-Quadratic Minimization Methods for Signal and Image Recovery
SIAM Journal on Scientific Computing
Iterative Methods for Toeplitz Systems (Numerical Mathematics and Scientific Computation)
Iterative Methods for Toeplitz Systems (Numerical Mathematics and Scientific Computation)
Deblurring Images: Matrices, Spectra, and Filtering (Fundamentals of Algorithms 3) (Fundamentals of Algorithms)
Cosine transform based preconditioners for total variation deblurring
IEEE Transactions on Image Processing
Convex half-quadratic criteria and interacting auxiliary variables for image restoration
IEEE Transactions on Image Processing
Nonlinear image recovery with half-quadratic regularization
IEEE Transactions on Image Processing
| Hi-index | 7.29 |
Image restoration is a fundamental problem in image processing. Except for many different filters applied to obtain a restored image in image restoration, a degraded image can often be recovered efficiently by minimizing a cost function which consists of a data-fidelity term and a regularization term. In specific, half-quadratic regularization can effectively preserve image edges in the recovered images and a fixed-point iteration method is usually employed to solve the minimization problem. In this paper, the Newton method is applied to solve the half-quadratic regularization image restoration problem. And at each step of the Newton method, a structured linear system of a symmetric positive definite coefficient matrix arises. We design two different decomposition-based block preconditioning matrices by considering the special structure of the coefficient matrix and apply the preconditioned conjugate gradient method to solve this linear system. Theoretical analysis shows the eigenvector properties and the spectral bounds for the preconditioned matrices. The method used to analyze the spectral distribution of the preconditioned matrix and the correspondingly obtained spectral bounds are different from those in the literature. The experimental results also demonstrate that the decomposition-based block preconditioned conjugate gradient method is efficient for solving the half-quadratic regularization image restoration in terms of the numerical performance and image recovering quality.