arXiv subjects

George Baravdish

Publications and source records attributed to George Baravdish.

9 recordsLinked to original sources

arXiv2026

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.

cs.CV↗

arXiv2026

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.

cs.CV↗

arXiv2026

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.

cs.CV↗

arXiv2026

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.

cs.CV↗

arXiv2026

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.

cs.CV↗

arXiv2022

Standalone Neural ODEs with Sensitivity Analysis

This paper presents the Standalone Neural ODE (sNODE), a continuous-depth neural ODE model capable of describing a full deep neural network. This uses a novel nonlinear conjugate gradient (NCG) descent optimization scheme for training, where the Sobolev gradient can be incorporated to improve smoothness of model weights. We also present a general formulation of the neural sensitivity problem and show how it is used in the NCG training. The sensitivity analysis provides a reliable measure of uncertainty propagation throughout a network, and can be used to study model robustness and to generate adversarial attacks. Our evaluations demonstrate that our novel formulations lead to increased robustness and performance as compared to ResNet models, and that it opens up for new opportunities for designing and developing machine learning with improved explainability.

cs.LG↗

arXiv2022

Learning via nonlinear conjugate gradients and depth-varying neural ODEs

The inverse problem of supervised reconstruction of depth-variable (time-dependent) parameters in a neural ordinary differential equation (NODE) is considered, that means finding the weights of a residual network with time continuous layers. The NODE is treated as an isolated entity describing the full network as opposed to earlier research, which embedded it between pre- and post-appended layers trained by conventional methods. The proposed parameter reconstruction is done for a general first order differential equation by minimizing a cost functional covering a variety of loss functions and penalty terms. A nonlinear conjugate gradient method (NCG) is derived for the minimization. Mathematical properties are stated for the differential equation and the cost functional. The adjoint problem needed is derived together with a sensitivity problem. The sensitivity problem can estimate changes in the network output under perturbation of the trained parameters. To preserve smoothness during the iterations the Sobolev gradient is calculated and incorporated. As a proof-of-concept, numerical results are included for a NODE and two synthetic datasets, and compared with standard gradient approaches (not based on NODEs). The results show that the proposed method works well for deep learning with infinite numbers of layers, and has built-in stability and smoothness.

cs.LG↗

arXiv2019

Iterative TV minimization on the graph

We define the space of functions of bounded variation ($BV$) on the graph. Using the notion of divergence of flows on graphs, we show that the unit ball of the dual space to $BV$ in the graph setting can be described as the image of the unit ball of the space $\ell^{\infty}$ by the divergence operator. Based on this result, we propose a new iterative algorithm to find the exact minimizer for the total variation (TV) denoising problem on the graph. The proposed algorithm is provable convergent and its performance on image denoising examples is compared with the Split Bregman and Primal-Dual algorithms as benchmarks for iterative methods and with BM3D as a benchmark for other state-of-the-art denoising methods. The experimental results show highly competitive empirical convergence rate and visual quality for the proposed algorithm.

math.OC↗

arXiv2019

Damped second order flow applied to image denoising

In this paper, we introduce a new image denoising model: the damped flow (DF), which is a second order nonlinear evolution equation associated with a class of energy functionals of image. The existence, uniqueness and regularization property of DF are proven. For the numerical implementation, based on the Störmer-Verlet method, a discrete damped flow, SV-DDF, is developed. The convergence of SV-DDF is studied as well. Several numerical experiments, as well as a comparison with other methods, are provided to demonstrate the feasibility and effectiveness of the SV-DDF.

math.NA↗