Parallel Algorithms for Solution of Nonlinear Diffusion Problems in Image Smoothing

Abstract

In this work we consider parallel algorithms for solution of nonlinear parabolic PDEs. First mathematical models describing nonlinear diffusion filters are presented. The finite‐volume method is used to approximate differential equations. Parallel algorithms are based on the domain decomposition method. The algorithms are implemented by using ParSol parallelization tool and a brief description of this tool is also presented. The efficiency of proposed parallel algorithms is investigated and results of the scalability analysis are given. Theoretical predictions are compared with results of computational experiments. Application of nonlinear diffusion filters for analysis of computer tomography images is discussed in the last section of the paper. Šiame darbe nagrinejami lygiagretieji algoritmai, kurie skirti netiesiniu nestacionariu difuzijos lygčiu sprendimui. Pirmiausia yra suformuluoti netiesiniu filtru matematiniai modeliai. Šie uždaviniai aproksimuoti baigtiniu tūriu schemomis. Lygiagretieji algoritmai konstruojami duomenu lygiagretumo metodu. Jie realizuoti autoriu sukurtu ParSolprogramavimo irankiu. Pateiktas trumpas šio irankio aprašymas. Ištirtas lygiagrečiuju algoritmu efektyvumas ir pateikti algoritmu išplečiamumo analizes rezultatai. Teorines išvados palygintos su skaičiavimo rezultatais. Netiesiniai difuziniai filtrai pritaikyti galvos kompiuteriniu tomogramu filtravimui.

Parallel LOD Scheme for 3D Parabolic Problem with Nonlocal Boundary Condition

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Web Application for Large-Scale Multidimensional Data Visualization

“…To achieve a high performance in a large-scale multidimensional data visualization, the parallel computing has to be exploited. Parallel applications, including scientific applications, are now widely executed on clusters and grids [5]. For the large-scale multidimensional data visualization, a high-performance parallel cluster has been used in our implementation.…”

Error Estimations for Total Variation Type Regularization

“…The Total Variation (TV) has been used extensively in the literature for decades in imaging sciences and a series of techniques have been dedicated to researching its choice of regularization parameter [21][22][23][24][25][26][27][28][29][30][31]; others [32,33] are developed based on this observation. Similar to [34], Total Variation can also smooth the signal of interest. Let H 2 be another Hilbert space.…”