Open AccessOptical image reconstruction based on the third-order diffusion equations
Author(s) -
Huabei Jiang
Publication year - 1999
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.4.000241
Subject(s) - tikhonov regularization , third order , iterative reconstruction , algorithm , computer science , diffusion equation , regularization (linguistics) , finite element method , void (composites) , mathematics , inverse problem , optics , mathematical analysis , physics , artificial intelligence , philosophy , materials science , theology , economy , economics , composite material , thermodynamics , service (business)
This paper presents a third-order diffusion equations-based optical image reconstruction algorithm. The algorithm has been implemented using finite element discretizations coupled with a hybrid regularization that combines both Marquardt and Tikhonov schemes. Numerical examples are used to compare between the third- and first-order reconstructions. The results show that the third-order reconstruction codes are more stable than the first-order codes, and are capable of reconstructing void-like regions. From the examples given, it has also been shown that the first-order codes fail to both qualitatively and quantitatively reconstruct the void-like regions.