George Baravdish

On tensor-based PDEs and their corresponding variational formulations with application to color image denoising

The case when a partial differential equation (PDE) can be considered as an Euler-Lagrange (E-L) equation of an energy functional, consisting of a data term and a smoothness term is investigated. We show the necessary conditions for a PDE to be the E-L equation for a corresponding functional. This energy functional is applied to a color image denoising problem and it is shown that the method compares favorably to current state-of-the-art color image denoising techniques.

Analysis of vehicular wireless channel communication via queueing theory model

The 4G standard Long Term Evolution (LTE) has been developed for high-bandwidth mobile access for todays data-heavy applications, consequently, a better experience for the end user. Since cellular communication is ready available, LTE communication has been designed to work at high speeds for vehicular communication. The challenge is that the protocols in LTE/LTE-Advanced should not only provide good packet delivery but also adapt to changes in the network topology due to vehicle volume and vehicular mobility. It is a critical requirement to ensure a seamless quality of experience ranging from safety to relieving congestion as deployment of LTE/LTE-Advanced become common. This requires learning how to improve the LTE/LTE-Advanced model to better appeal to a wider base and move toward additional solutions. In this paper we present a feasibility analysis for performing vehicular communication via a queueing theory approach based on a multi-server queue using real LTE traffic. A M/M/m model is employed to evaluate the probability that a vehicle finds all channels busy, as well as to derive the expected waiting times and the expected number of channel switches. Also, when a base station (eNB) becomes overloaded with a single-hop, a multi-hop rerouting optimization approach is presented.

A Tensor Variational Formulation of Gradient Energy Total Variation

We present a novel variational approach to a tensor-based total variation formulation which is called gradient energy total variation, GETV. We introduce the gradient energy tensor [6] into the GETV and show that the corresponding Euler-Lagrange (E-L) equation is a tensor-based partial differential equation of total variation type. Furthermore, we give a proof which shows that GETV is a convex functional. This approach, in contrast to the commonly used structure tensor, enables a formal derivation of the corresponding E-L equation. Experimental results suggest that GETV compares favourably to other state of the art variational denoising methods such as extended anisotropic diffusion (EAD)[1] and total variation (TV) [18] for gray-scale and colour images.

Targeted Iterative Filtering

The assessment of image denoising results depends on the respective application area, i.e. image compression, still-image acquisition, and medical images require entirely different behavior of the applied denoising method. In this paper we propose a novel, nonlinear diffusion scheme that is derived from a linear diffusion process in a value space determined by the application. We show that application-driven linear diffusion in the transformed space compares favorably with existing nonlinear diffusion techniques.

Higher Precision in Volume Haptics through Subdivision of Proxy Movements

Volume haptics has become an increasingly popular way of adding guidance and improving information bandwidth in scientific visualization. State-of-the-art methods, however, use linear equations, which allows for a precision that can be insufficient in some circumstances. This paper describes how step-length subdivision can be used to improve precision even though these methods do not use integration steps in its usual meaning.

On Backward p(x)-Parabolic Equations for Image Enhancement

In this study, we investigate the backward p(x)-parabolic equation as a new methodology to enhance images. We propose a novel iterative regularization procedure for the backward p(x)-parabolic equation based on the nonlinear Landweber method for inverse problems. The proposed scheme can also be extended to the family of iterative regularization methods involving the nonlinear Landweber method. We also investigate the connection between the variable exponent p(x) in the proposed energy functional and the diffusivity function in the corresponding Euler-Lagrange equation. It is well known that the forward problems converges to a constant solution destroying the image. The purpose of the approach of the backward problems is twofold. First, solving the backward problem by a sequence of forward problems, we obtain a smooth image which is denoised. Second, by choosing the initial data properly, we try to reduce the blurriness of the image. The numerical results for denoising appear to give improvement over standard methods as shown by preliminary results.

Numerical analysis of an industrial power saving mechanism in LTE

The 4G standard Long Term Evolution (LTE) utilizes discontinuous reception (DRX) to extend the user equipments battery lifetime. DRX permits an idle UE to power off the radio receiver for two predefined sleep period and then wake up to receive the next paging message. Two major basic power saving models proposed to data are the 3GPP ETSI model and industrial DRX model proposed by Nokia. While previous studies have investigated power saving with the 3GPP ETSI models, the industrial DRX model has not been considered for analytical studies to date. Thus, there is a need to optimize the DRX parameters in the industrial model so as to maximize power saving without incurring network reentry and packet delays. In this paper, we take an overview of various static DRX cycles of the LTE/LTE-Advanced power saving mechanisms by modelling the system with bursty packet data traffic using a semi-Markov process. Using this analytical model, we will show the tradeoff relationship between the power saving and wake-up delay performance in the industrial model.

PDE-SVD based audio denoising

In this paper we present a new method for denoising audio signals. The method is based on the Singular Value Decomposition (SVD) of the frame matrix representing the signal in the Overlap Add decomposition. Denoising is performed by modifying both the singular values, using a tapering model, and the singular vectors of the representation, using a nonlinear PDE method. The performance of the method is evaluated and compared with denoising obtained by filtering.

Mapping-Based Image Diffusion

In this work, we introduce a novel tensor-based functional for targeted image enhancement and denoising. Via explicit regularization, our formulation incorporates application-dependent and contextual information using first principles. Few works in literature treat variational models that describe both application-dependent information and contextual knowledge of the denoising problem. We prove the existence of a minimizer and present results on tensor symmetry constraints, convexity, and geometric interpretation of the proposed functional. We show that our framework excels in applications where nonlinear functions are present such as in gamma correction and targeted value range filtering. We also study general denoising performance where we show comparable results to dedicated PDE-based state-of-the-art methods.

Using channel representations in regularization terms a case study on image diffusion

In this work we propose a novel non-linear diffusion filtering approach for images based on their channel representation. To derive the diffusion update scheme we formulate a novel energy functional using a soft-histogram representation of image pixel neighborhoods obtained from the channel encoding. The resulting Euler-Lagrange equation yields a non-linear robust diffusion scheme with additional weighting terms stemming from the channel representation which steer the diffusion process. We apply this novel energy formulation to image reconstruction problems, showing good performance in the presence of mixtures of Gaussian and impulse-like noise, e.g. missing data. In denoising experiments of common scalar-valued images our approach performs competitive compared to other diffusion schemes as well as state-of-the-art denoising methods for the considered noise types.