# 01-08-2015

**New paper in the IEEE Transactions of signal Processing****Authors:**G. Papageorgiou, P Bouboulis, S. Theodoridis**Title:**Robust Linear Regression Analysis - A Greedy approachIn the following work, the task of robust estimation in the presence of outliers is presented. Despite the fact that, the problem has been stated a few decades ago and solved using classic (considered nowadays) methods, modern approaches have made notable contributions to the problem. In the present manuscript, an alternative approach is considered. Outliers are explicitly modeled by employing sparsity arguments and a novel efficient algorithm (Greedy Algorithm for Robust Denoising - (GARD)), based on the greedy Orthogonal Matching Pursuit (OMP) scheme, is derived. The case where only outliers are present has been studied separately, where bounds on the Restricted Isometry Property, guarantees that the recovery of the signal via (GARD) is exact. Moreover, theoretical results concerning error bounds and the recovery of the support of the solution in the case of additional bounded noise are discussed. Finally, we provide extensive simulations, which verify the comparative advantages of the new technique.

# 04-04-2014

**New paper accepted in CIP 2014****Authors:**Pantelis Bouboulis, G. Papageorgiou, S. Theodoridis**Title:**Robust Image Denoising in RKHS via Orthogonal Matching PursuitWe present a robust method for the image denoising task based on kernel ridge regression and sparse modeling. Added noise is assumed to consist of two parts. One part is impulse noise assumed to be sparse (outliers), while the other part is bounded noise. The noisy image is divided into small regions of interest, whose pixels are regarded as points of a two-dimensional surface. A kernel based ridge regression method, whose parameters are selected adaptively, is employed to fit the data, whereas the outliers are detected via the use of the increasingly popular orthogonal matching pursuit (OMP) algorithm. To this end, a new variant of the OMP rationale is employed that has the additional advantage to automatically terminate, when all outliers have been selected.

# 15-02-2011

**New paper accepted in Elsevier's Computational and Applied Mathematics****Authors:**Pantelis Bouboulis, M. Mavroforakis**Title:**Reproducing Kernel Hilbert Spaces and Fractal InterpolationFinally, this paper has been accepted. This is the first time that fractals are used to construct kernels. Myself and Dr. Mavroforakis hope that this work will pave the road for applying fractal-based kernels in many real problems.

# 16-11-2010

**New paper accepted in IEEE Transactions on Signal Processing****Authors:**Pantelis Bouboulis, Sergios Theodoridis**Title:**Extension of Wirtinger?s Calculus to Reproducing Kernel Hilbert Spaces and the Complex Kernel LMSI was notified that my paper "Extension of Wirtinger?s Calculus to Reproducing Kernel Hilbert Spaces and the Complex Kernel LMS" has been accepted for publication in the March or April 2011 issue of the IEEE Transactions on Signal Processing. You may find the preprint version at Arxiv. If you are interested in Wirtinger's Calculus you may find useful my detailed notes on the subject.

# 26-07-2010

**ICPR 2010 Best paper award****Authors:**Pantelis Bouboulis, K. Slavakis, Sergios Theodoridis**Title:**Edge Preserving Image Denoising in Reproducing kernel Hilbert SpacesThis work has been selected for the

**Best Scientific Paper Award**(Track III: Signal, Speech, Image and Video Processing) click here for details.

# 29-06-2010

**New paper accepted in the 20th International Conference on Artificial Neural Networks (ICANN 2010)****Authors:**Pantelis Bouboulis, Sergios Theodoridis**Title:**The Complex Gaussian Kernel and the Complex Kernel LMS algorithm

# 28-05-2010

**New paper accepted in the Machine Learning for Signal Processing 2010 (MLSP 2010) Conference****Authors:**Pantelis Bouboulis, Sergios Theodoridis**Title:**Extension of Wirtinger Calculus in RKH spaces and the Complex Kernel LMS

# 25-05-2010

**New paper published in the IEEE Transactions On Image Processing.****Authors:**Pantelis Bouboulis, K. Slavakis, Sergios Theodoridis**Title:**Adaptive Kernel-based Image Denoising employing Semi-Parametric Regularization**Abstract:**The main contribution of this paper is the development of a novel approach, based on the theory of Reproducing Kernel Hilbert Spaces (RKHS), for the problem of Noise Removal in the spatial domain. The proposed methodology has the advantage that it is able to remove any kind of additive noise (impulse, gaussian, uniform, e.t.c.) from any digital image, in contrast to the most commonly used denoising techniques, which are noise-dependent. The problem is cast as an optimization task in a RKHS, by taking advantage of the celebrated Representer Theorem in its semi-parametric formulation. The semiparametric formulation, although known in theory, has so far found limited, to our knowledge, application. However, in the image denoising problem its use is dictated by the nature of the problem itself. The need for edge preservation naturally leads to such a modeling. Examples verify that in the presence of gaussian noise the proposed methodology performs well compared to wavelet based technics and outperforms them significantly in the presence of impulse or mixed noise.

# 08-04-2010

**New paper accepted in the ICPR 2010 conference****Authors:**Pantelis Bouboulis, K. Slavakis, Sergios Theodoridis**Title:**Edge Preserving Image Denoising in Reproducing kernel Hilbert SpacesThis is a presentation of the article that will be published in the IEEE Transactions of Image Processing with title "Adaptive Kernel-based Image Denoising employing Semi-Parametric Regularization".

# 15-01-2010

**New paper accepted in the IEEE Transactions of Image Processing**Today I received the letter of acceptance for this manuscript.

**Title:**Adaptive Kernel-based Image Denoising employing Semi-Parametric Regularization.

# 12-01-2010

**New paper published by the Journal of Mathematical Sciences: Advances and Applications****Title:**Modeling Discrete Sequences with Fractal interpolation Functions of higher order**Abstract:**A new construction of fractal interpolation surfaces, using solutions of partial differential equations, is presented. We consider a set of interpolation points placed on a rectangular grid and a specific PDE, such that its Dirichlet's problem is uniquely solvable inside any given orthogonal region. We solve the PDE, using numerical methods, for a number of regions, to construct two functions H and B, which are then used to produce the fractal surface, as the attractor of an appropriately chosen recurrent iterated function system.

# 08-01-2010

**New paper published by SRX Mathematics**SRX Mathematics is a relatively new open access journal. Visit its web site here.

**Title:**Construction of Fractal surfaces via solutions of Partial Differential Equations**Abstract:**A new construction of fractal interpolation surfaces, using solutions of partial differential equations, is presented. We consider a set of interpolation points placed on a rectangular grid and a specific PDE, such that its Dirichlet's problem is uniquely solvable inside any given orthogonal region. We solve the PDE, using numerical methods, for a number of regions, to construct two functions H and B, which are then used to produce the fractal surface, as the attractor of an appropriately chosen recurrent iterated function system.