An efficient algorithm of total variation regularization in the two-dimensional case

2020 ◽  
Author(s):  
Artyom Makovetskii ◽  
Sergei Voronin ◽  
Vitaly Kober ◽  
Aleksei Voronin
Keyword(s):  
Total Variation ◽  
Efficient Algorithm ◽  
Dimensional Case ◽  
Total Variation Regularization ◽  
Two Dimensional

The formation of gas hydrates under shock wave impact on the bubble media (two-dimensional case)

2010 ◽  
Vol 7 ◽  
pp. 90-97
Author(s):  
M.N. Galimzianov ◽  
I.A. Chiglintsev ◽  
U.O. Agisheva ◽  
V.A. Buzina
Keyword(s):  
Shock Wave ◽  
Gas Hydrates ◽  
Hydrate Formation ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Wave Impact ◽  
Bubble Liquid ◽  
One Dimensional ◽  
Bubble Media ◽  
Main Factors

Formation of gas hydrates under shock wave impact on bubble media (two-dimensional case) The dynamics of plane one-dimensional shock waves applied to the available experimental data for the water–freon media is studied on the base of the theoretical model of the bubble liquid improved with taking into account possible hydrate formation. The scheme of accounting of the bubble crushing in a shock wave that is one of the main factors in the hydrate formation intensification with increasing shock wave amplitude is proposed.

Regions-based Two-dimensional Continua: The Euclidean Case

2018 ◽  
Author(s):  
Geoffrey Hellman ◽  
Stewart Shapiro
Keyword(s):  
Mathematical Induction ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Entire Space ◽  
Euclidean Case ◽  
Free Basis ◽  
One Dimensional ◽  
Archimedean Property ◽  
The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

scholarly journals An Improved Particle Swarm Optimization Based on Total Variation Regularization and Projection Constraint with Applications in Ground-Penetrating Radar Inversion: A Model Simulation Study

2021 ◽  
Vol 13 (13) ◽  
pp. 2514
Author(s):  
Qianwei Dai ◽  
Hao Zhang ◽  
Bin Zhang
Keyword(s):  
Particle Swarm Optimization ◽  
Total Variation ◽  
Ground Penetrating Radar ◽  
Particle Swarm ◽  
Premature Convergence ◽  
Total Variation Regularization ◽  
Interface Model ◽  
Swarm Optimization ◽  
Tv Regularization ◽  
Ground Penetrating

The chaos oscillation particle swarm optimization (COPSO) algorithm is prone to binge trapped in the local optima when dealing with certain complex models in ground-penetrating radar (GPR) data inversion, because it inherently suffers from premature convergence, high computational costs, and extremely slow convergence times, especially in the middle and later periods of iterative inversion. Considering that the bilateral connections between different particle positions can improve both the algorithmic searching efficiency and the convergence performance, we first develop a fast single-trace-based approach to construct an initial model for 2-D PSO inversion and then propose a TV-regularization-based improved PSO (TVIPSO) algorithm that employs total variation (TV) regularization as a constraint technique to adaptively update the positions of particles. B by adding the new velocity variations and optimal step size matrices, the search range of the random particles in the solution space can be significantly reduced, meaning blindness in the search process can be avoided. By introducing constraint-oriented regularization to allow the optimization search to move out of the inaccurate region, the premature convergence and blurring problems can be mitigated to further guarantee the inversion accuracy and efficiency. We report on three inversion experiments involving multilayered, fluctuated terrain models and a typical complicated inner-interface model to demonstrate the performance of the proposed algorithm. The results of the fluctuated terrain model show that compared with the COPSO algorithm, the fitness error (MAE) of the TVIPSO algorithm is reduced from 2.3715 to 1.0921, while for the complicated inner-interface model the fitness error (MARE) of the TVIPSO algorithm is reduced from 1.9539 to 1.5674.

A new nonlinear reconstruction method based on total variation regularization of neutron penumbral imaging

2011 ◽  
Vol 82 (9) ◽  
pp. 093504 ◽  
Author(s):  
Weixin Qian ◽  
Shuangxi Qi ◽  
Wanli Wang ◽  
Jinming Cheng ◽  
Dongbing Liu
Keyword(s):  
Total Variation ◽  
Total Variation Regularization ◽  
Reconstruction Method ◽  
Penumbral Imaging
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