Numerical Methods for Total Variation and Besov Smoothing

Applied and Computational Mathematics Seminar
Monday, April 13, 2009 - 1:00pm for 1 hour (actually 50 minutes)
Skiles 255
Stacey Levine – Duquesne University
Sung Ha Kang
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.