Numerical Methods for Total Variation and Besov Smoothing

Applied and Computational Mathematics Seminar
Monday, April 13, 2009 - 1:00pm
1 hour (actually 50 minutes)
Skiles 255
Duquesne University
We present new finite difference approximations for solving
variational problems using the TV and Besov smoothness penalty
functionals. The first approach reduces oversmoothing and anisotropy
found in common discrete approximations of the TV functional. The
second approach reduces the staircasing effect that arises from TV
type smoothing. The algorithms converge and can be sped up using a
multiscale algorithm. Numerical examples demonstrate both the
qualitative and quantitative behavior of the solutions.