Mathematics
and Computer Science Speaker Series
California State University, Stanislaus
Date: Friday,
March 2, 2012
Time: 4:00 - 5:00 p.m
Room: P-164
Speaker: Jason
Barnett
Title: Derivations of Euler-Lagrange Equations in Imaging
Abstract: In imaging, it is necessary to minimize functionals to
construct a smoothed image close to the original. This is
best accomplished by using calculus of variations, specifically the
Gateaux variation and Euler-Lagrange equations. In
this talk, I will present and compare two methods of deriving
Euler-Lagrange equations, one by directly computing when
the Gateaux variation is equal to zero for all test functions on the
necessary set, and the other by using the general Euler-Lagrange
equation. Using these methods, I will demonstrate an elementary example
and then apply this concept to a specific imaging model.