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In various applications, i. e., astronomical imaging, electron microscopy, and tomography, images are often damaged by Poisson noise. At the same time, the thermal motion leads to Gaussian noise. Therefore, in such applications, the image is usually corrupted by mixed Poisson – Gaussian noise.

In this paper, we propose a novel method for recovering images corrupted by mixed Poisson – Gaussian noise. In the proposed method, we develop a total variation-based model connected with the nonconvex function and the total generalized variation regularization, which overcomes the staircase artifacts and maintains neat edges.

Numerically, we employ the primal-dual method combined with the classical iteratively reweighted $l_1$ algorithm to solve our minimization problem. Experimental results are provided to demonstrate the superiority of our proposed model and algorithm for mixed Poisson – Gaussian removal to state-of-the-art numerical methods.

WENO schemes (weighted, essentially non oscillating) are currently having a wide range of applications as approximate high order schemes for discontinuous solutions of partial differential equations. These schemes are used for direct numerical simulation (DNS) and large eddy simmulation in the gas dynamic problems, problems for DNS in MHD and even neutron kinetics. This work is dedicated to clarify some characteristics of WENO schemes and numerical simulation of specific tasks. Results of the simulations can be used to clarify the field of application of these schemes. The first part of the work contained proofs of the approximation properties, stability and convergence of WENO5, WENO7, WENO9, WENO11 and WENO13 schemes. In the second part of the work the modified wave number analysis is conducted that allows to conclude the dispersion and dissipative properties of schemes. Further, a numerical simulation of a number of specific problems for hyperbolic equations is conducted, namely for advection equations (one-dimensional and two-dimensional), Hopf equation, Burgers equation (with low dissipation) and equations of non viscous gas dynamics (onedimensional and two-dimensional). For each problem that is implying a smooth solution, the practical calculation of the order of approximation via Runge method is performed. The influence of a time step on nonlinear properties of the schemes is analyzed experimentally in all problems and cross checked with the first part of the paper. In particular, the advection equations of a discontinuous function and Hopf equations show that the failure of the recommendations from the first part of the paper leads first to an increase in total variation of the solution and then the approximation is decreased by the non-linear dissipative mechanics of the schemes. Dissipation of randomly distributed initial conditions in a periodic domain for one-dimensional Burgers equation is conducted and a comparison with the spectral method is performed. It is concluded that the WENO7–WENO13 schemes are suitable for direct numerical simulation of turbulence. At the end we demonstrate the possibility of the schemes to be used in solution of initial-boundary value problems for equations of non viscous gas dynamics: Rayleigh–Taylor instability and the reflection of the shock wave from a wedge with the formation a complex configuration of shock waves and discontinuities.

We present a physico-mathematical statement of coupled geometrical and gas dynamics problem of intrachamber processes simulation and calculation of main internal ballistics characteristics of solid rocket motors in axisymmetric approximation. Method and numerical algorithm of solving the problem are described in this paper. We track the propellant burning surface using the level set method. This method allows us to implicitly represent the surface on a fixed Cartesian grid as zero-level of some function. Two-dimensional gas-dynamics equations describe a flow of combustion products in a solid rocket motor. Due to inconsistency of domain boundaries and nodes of computational grid, presence of ghost points lying outside the computational domain is taken into account. For setting the values of flow parameters in ghost points, we use the inverse Lax – Wendroff procedure. We discretize spatial derivatives of level set and gas-dynamics equations with standard WENO schemes of fifth and third-order respectively and time derivatives using total variation diminishing Runge –Kutta methods. We parallelize the presented numerical algorithm using CUDA technology and further optimize it with regard to peculiarities of graphics processors architecture.

Created software package is used for calculating internal ballistics characteristics of nozzleless solid rocket motor during main firing phase. On the base of obtained numerical results, we discuss efficiency of parallelization using CUDA technology and applying considered optimizations. It has been shown that implemented parallelization technique leads to a significant acceleration in comparison with central processes. Distributions of key parameters of combustion products flow in different periods of time have been presented in this paper. We make a comparison of obtained results between quasione-dimensional approach and developed numerical technique.

Image denoising is one of the fundamental problems in digital image processing. This problem usually refers to the reconstruction of an image from an observed image degraded by noise. There are many factors that cause this degradation such as transceiver equipment, or environmental influences, etc. In order to obtain higher quality images, many methods have been proposed for image denoising problem. Most image denoising method are based on total variation (TV) regularization to develop efficient algorithms for solving the related optimization problem. TV-based models have become a standard technique in image restoration with the ability to preserve image sharpness.

In this paper, we focus on Poisson noise usually appearing in photon-counting devices. We propose an effective regularization model based on combination of first-order and fractional-order total variation for image reconstruction corrupted by Poisson noise. The proposed model allows us to eliminate noise while edge preserving. An efficient alternating minimization algorithm is employed to solve the optimization problem. Finally, provided numerical results show that our proposed model can preserve more details and get higher image visual quality than recent state-of-the-art methods.

The equilibrium configurations of charged electrons, confined in the hard disk potential, are analysed by means of the hybrid numerical algorithm. The algorithm is based on the interpolation formulas, that are obtained from the analysis of the equilibrium configurations, provided by the variational principle developed in the circular model. The solution of the nonlinear equations of the circular model yields the formation of the shell structure which is composed of the series of rings. Each ring contains a certain number of particles, which decreases as one moves from the boundary ring to the central one. The number of rings depends on the total number of electrons. The interpolation formulas provide the initial configurations for the molecular dynamics calculations. This approach makes it possible to significantly increase the speed at which an equilibrium configuration is reached for an arbitrarily chosen number of particles compared to the Metropolis annealing simulation algorithm and other algorithms based on global optimization methods.

Accurate segmentation of liver plays important in contouring during diagnosis and the planning of treatment. Imaging technology analysis and processing are wide usage in medical diagnostics, and therapeutic applications. Liver segmentation referring to the process of automatic or semi-automatic detection of liver image boundaries. A major difficulty in segmentation of liver image is the high variability as; the human anatomy itself shows major variation modes. In this paper, a proposed approach for computed tomography (CT) liver segmentation is presented by combining exponential entropy and fuzzy c-partition. Entropy concept has been utilized in various applications in imaging computing domain. Threshold techniques based on entropy have attracted a considerable attention over the last years in image analysis and processing literatures and it is among the most powerful techniques in image segmentation. In the proposed approach, the computed tomography (CT) of liver is transformed into fuzzy domain and fuzzy entropies are defined for liver image object and background. In threshold selection procedure, the proposed approach considers not only the information of liver image background and object, but also interactions between them as the selection of threshold is done by find a proper parameter combination of membership function such that the total fuzzy exponential entropy is maximized. Differential Evolution (DE) algorithm is utilizing to optimize the exponential entropy measure to obtain image thresholds. Experimental results in different CT livers scan are done and the results demonstrate the efficient of the proposed approach. Based on the visual clarity of segmented images with varied threshold values using the proposed approach, it was observed that liver segmented image visual quality is better with the results higher level of threshold.