Stanislav Harizanov

Epigraphical Projection for Solving Least Squares Anscombe Transformed Constrained Optimization Problems

This paper deals with the restoration of images corrupted by a non-invertible or ill-conditioned linear transform and Poisson noise. Poisson data typically occur in imaging processes where the images are obtained by counting particles, e.g., photons, that hit the image support. By using the Anscombe transform, the Poisson noise can be approximated by an additive Gaussian noise with zero mean and unit variance. Then, the least squares difference between the Anscombe transformed corrupted image and the original image can be estimated by the number of observations. We use this information by considering an Anscombe transformed constrained model to restore the image. The advantage with respect to corresponding penalized approaches lies in the existence of a simple model for parameter estimation. We solve the constrained minimization problem by applying a primal-dual algorithm together with a projection onto the epigraph of a convex function related to the Anscombe transform. We show that this epigraphical projection can be efficiently computed by Newton’s methods with an appropriate initialization. Numerical examples demonstrate the good performance of our approach, in particular, its close behaviour with respect to the I-divergence constrained model.

Normal Multi-scale Transforms for Curves

Extending upon Daubechies et al. (Constr. Approx. 20:399–463, 2004) and Runborg (Multiscale Methods in Science and Engineering, pp. 205–224, 2005), we provide the theoretical analysis of normal multi-scale transforms for curves with general linear predictor S, and a more flexible choice of normal directions. The main parameters influencing the asymptotic properties (convergence, decay estimates for detail coefficients, smoothness of normal re-parametrization) of this transform are the smoothness of the curve, the smoothness of S, and its order of exact polynomial reproduction. Our results give another indication why approximating S may not be the first choice in compression applications of normal multi-scale transforms.

Supervised 2-Phase Segmentation of Porous Media with Known Porosity

Porous media segmentation is a nontrivial and often quite inaccurate process, due to the highly irregular structure of the segmentation phases and the huge interaction among them. In this paper we perform a 2-class segmentation of a gray-scale 3D image under the restriction that the number of voxels within the phases are a priori fixed. Two parallel algorithms, based on the graph 2-Laplacian model [1] are proposed, implemented, and numerically tested.

Optimal solvers for linear systems with fractional powers of sparse SPD matrices: Optimal Solvers for Linear Systems with Fractional Powers of Sparse SPD Matrices

In this paper we consider efficient algorithms for solving the algebraic equation

Globally convergent adaptive normal multi-scale transforms

{\mathcal A}^\alpha {\bf u}={\bf f}

Positive Approximations of the Inverse of Fractional Powers of SPD M-Matrices

,

Noise Removal and Feature Extraction of 2D CT Radiographic Images

0< \alpha <1

Fast Constrained Image Segmentation Using Optimal Spanning Trees

, where

Sex estimation by size and shape of foramen magnum based on CT imaging

{\mathcal A}

Performance analysis of a parallel algorithm for restoring large-scale CT images

is a symmetric and positive definite matrix obtained form finite difference or finite element approximations of second order elliptic problems in