Keywords: Edge-preserving regularization Salt-and-pepper impulse noise Cardinal splines Expeditious algorithm Image de-noising Cardinal spline interpolation Edge preservation Two-phase noise removal a b s t r a c t This work proposes a faster and an efficient way to remove salt-and-pepper impulse noise and edge-preserving regularization of the henceforth obtained image. In this paper, we propos...

This work deals with an extension of the standard recursive least squares (RLS) algorithm. It allows to prune irrelevant coefficients of a linear adaptive filter with sparse impulse response and it provides a regularization method with automatic adjustment of the regularization parameter. New update equations for the inverse auto-correlation matrix estimate are derived that account for the cont...

Standard video compression techniques apply motion-compensated prediction combined with transform coding of the prediction error. In the context of prediction with fractional-pel motion vector resolution it was shown, that aliasing components contained in an image signal are limiting the prediction accuracy obtained by motion compensation. In order to consider aliasing, quantisation and motion ...

Image restoration from degraded images lies at the foundation of image processing, pattern recognition, and computer vision, so it has been extensively studied. A large number of image restoration filters have been devised so far. It is known that a certain filter works excellently for a certain type of original image or degradation. However, the same filter may not be suitable for other images...

The solution, x, of the linear system of equations Ax ≈ b arising from the discretization of an ill-posed integral equation g(s) = ∫ H(s, t)f(t) dt with a square integrable kernel H(s, t) is considered. The Tikhonov regularized solution x(λ) approximating the Galerkin coefficients of f(t) is found as the minimizer of J(x) = {‖Ax− b‖2 +λ‖Lx‖2}, where b is given by the Galerkin coefficients of g(...

Many iterative methods that are used to solve Ax = b can be derived as quasi-Newton methods for minimizing the quadratic function 1 2 xAAx−xAb. In this paper, several such methods are considered, including conjugate gradient least squares (CGLS), Barzilai-Borwein (BB), residual norm steepest descent (RNSD) and Landweber (LW). Regularization properties of these methods are studied by analyzing t...

-Layered architecture is proposed for solving a class o f regularization problems in image processing. There are two major hurdles in the implementation of regularization filters with second or higher order smoothness constraints: ( a ) Stability: With second or higher order constraints, a direct implementation of a regularization filter necessitates negative conductance which, in turn, gives r...

We present a multigrid algorithm for the solution of distributed parameter inverse problems constrained by variable-coefficient linear parabolic partial differential equations. We consider problems in which the inversion variable is a function of space only; for stability we use an L2 Tikhonov regularization. The main feature of our algorithm is that its convergence rate is mesh-independent—eve...

Methods for `1-type regularization have been widely used in Gaussian graphical model selection tasks to encourage sparse structures. However, often we would like to include more structural information than mere sparsity. In this work, we focus on learning so-called “scale-free” models, a common feature that appears in many real-work networks. We replace the `1 regularization with a power law re...