scholarly journals A General Total Variation Minimization Theorem for Compressed Sensing Based Interior Tomography

2009 ◽  
Vol 2009 ◽  
pp. 1-3 ◽  
Author(s):  
Weimin Han ◽  
Hengyong Yu ◽  
Ge Wang
Keyword(s):  
Compressed Sensing ◽  
Total Variation ◽  
General Theorem ◽  
Region Of Interest ◽  
Delta Function ◽  
Piecewise Constant Function ◽  
Mathematical Tool ◽  
Total Variation Minimization ◽  
Piecewise Constant ◽  
Dirac Delta

Recently, in the compressed sensing framework we found that a two-dimensional interior region-of-interest (ROI) can be exactly reconstructed via the total variation minimization if the ROI is piecewise constant (Yu and Wang, 2009). Here we present a general theorem charactering a minimization property for a piecewise constant function defined on a domain in any dimension. Our major mathematical tool to prove this result is functional analysis without involving the Dirac delta function, which was heuristically used by Yu and Wang (2009).

scholarly journals Optimization of STEM‐HAADF Electron Tomography Reconstructions by Parameter Selection in Compressed Sensing Total Variation Minimization‐Based Algorithms

2020 ◽  
Vol 37 (6) ◽  
pp. 2000070
Author(s):  
Juan M. Muñoz‐Ocaña ◽  
Ainouna Bouziane ◽  
Farzeen Sakina ◽  
Richard T. Baker ◽  
Ana B. Hungría ◽  
...  
Keyword(s):  
Compressed Sensing ◽  
Total Variation ◽  
Electron Tomography ◽  
Parameter Selection ◽  
Total Variation Minimization

scholarly journals On the calculus of Dirac delta function with some applications in classical electrodynamics

2021 ◽  
Vol 18 (2 Jul-Dec) ◽  
pp. 020205
Author(s):  
Milan S. Kovacevic ◽  
Miroslav R. Jovanovic ◽  
Marko M. Milosevic
Keyword(s):  
Charge Density ◽  
Point Charge ◽  
Delta Function ◽  
Analytical Framework ◽  
Dirac Delta Function ◽  
Classical Electrodynamics ◽  
Mathematical Tool ◽  
Point Dipole ◽  
Dirac Delta ◽  
Physics Curriculum

The Dirac delta function is a concept that is useful throughout physics as a standard mathematical tool that appears repeatedly in the undergraduate physics curriculum including electrodynamics, optics, and quantum mechanics. Our analysis was guided by an analytical framework focusing on how students activate, construct, execute, and reflect on the Dirac delta function in the context of classical electrodynamics problems solving. It’s applications in solving the charge density associated with a point charge as well as electrostatic point dipole field, for more advanced situations to describe the charge density of hydrogen atom were presented.

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