Abstract
A new deblurring and denoising algorithm is proposed, for isotropic total variation-based image restoration. The algorithm consists of an efficient solver for the nonlinear system and an acceleration strategy for the outer iteration. For the nonlinear system, the split Bregman method is used to convert it into linear system, and an algebraic multigrid method is applied to solve the linearized system. For the outer iteration, we have conducted formal convergence analysis to determine an auxiliary linear term that significantly stabilizes and accelerates the outer iteration. Numerical experiments demonstrate that our algorithm for deblurring and denoising problems is efficient.
Highlights
The purpose of image restoration is to recover original image u from an observed data z from the relation z = Ku + n, (1)where K is a known linear blurring operator and u is a Gaussian white noise
We propose an efficient and rapid algorithm for minimization problem (2) rather than solving the Euler-Lagrange equation (3) directly which combines the split Bregman method, the algebraic multigrid method, and Krylov subspace acceleration
We consider the combination of the two methods, and get a new denoising algorithm which is the split Bregman method based on algebraic multigrid (AMG)
Summary
Zuo and Lin [6] proposed a generalized accelerated proximal gradient (GAPG) approach for solving TV-based image restoration problems by replacing the Lipschitz constant with an appropriate positive-definite matrix, resulting in faster convergence, and the TV regularization can be either isotropic or anisotropic. We propose an efficient and rapid algorithm for minimization problem (2) rather than solving the Euler-Lagrange equation (3) directly which combines the split Bregman method, the algebraic multigrid method, and Krylov subspace acceleration. We have developed a stabilizing technique adapted to the blur operator K This is done by adding a linear term on both sides of the equation [23].
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