Structure Preserving Preconditioners for Image Deblurring

Negative Results for Multilevel Preconditioners in Image Deblurring

A one-dimensional deconvolution problem is discretized and certain multilevel preconditioned iterative methods are applied to solve the resulting linear system. The numerical results suggest that multilevel multiplicative preconditioners may have no advantage over two-level mul-tiplicative preconditioners. In fact, in the numerical experiments they perform worse than comparable two-level precon...

Spectral analysis and structure preserving preconditioners for fractional diffusion equations

where α ∈ (1, 2) is the fractional derivative order, f(x, t) is the source term, ∂u(x,t) ∂±x are the right-handed (+) and the left-handed (-) fractional derivatives and the nonnegative functions d±(x, t) are the diffusion coefficients. The FDEs emerges in many topics such as image processing and turbolent flow and are used to describe diffusion phenomena that cannot be modeled by the second ord...

Performance of Three Preconditioners for Image Deblurring Problem in Primal-Dual Formulation

In this paper, we consider the generalized saddle point linear system of equations which is obtained from discretizing the Euler Lagrange equations associated with image debulrring problem. This system is ill-conditioned and is of huge size. Moreover, the (2,2) block of the coefficient matrix of this system contains summation of two terms. One of these terms is a product of a Toepelitz matrix w...

Structure Preserving Image Smoothing

Fast Preconditioners for Total Variation Deblurring with Antireflective Boundary Conditions

In recent works several authors have proposed the use of precise boundary conditions (BCs) for blurring models and they proved that the resulting choice (Neumann or reflective, antireflective) leads to fast algorithms both for deblurring and for detecting the regularization parameters in presence of noise. When considering a symmetric point spread function, the crucial fact is that such BCs are...