Image Processing Variations with Analytic Kernels

Details Image Processing Variations with Analytic Kernels Image Processing Variations with Analytic Kernels

2012-04-05

arxiv.org/abs/1204.1097v1

Mathematics

Analysis of PDEs

18 pages

Scientific paper

Let $f\in L^1(\R^d)$ be real. The Rudin-Osher-Fatemi model is to minimize $\|u\|_{\dot{BV}}+\lambda\|f-u\|_{L^2}^2$, in which one thinks of $f$ as a given image, $\lambda > 0$ as a "tuning parameter", $u$ as an optimal "cartoon" approximation to $f$, and $f-u$ as "noise" or "texture". Here we study variations of the R-O-F model having the form $\inf_u\{\|u\|_{\dot{BV}}+\lambda \|K*(f-u)\|_{L^p}^q\}$ where $K$ is a real analytic kernel such as a Gaussian. For these functionals we characterize the minimizers $u$ and establish several of their properties, including especially their smoothness properties. In particular we prove that on any open set on which $u \in W^{1,1}$ and $\nabla u \neq 0$ almost every level set $\{u =c\}$ is a real analytic surface. We also prove that if $f$ and $K$ are radial functions then every minimizer $u$ is a radial step function.

Affiliated with

Also associated with

No associations

Rating

Image Processing Variations with Analytic Kernels does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Image Processing Variations with Analytic Kernels, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Image Processing Variations with Analytic Kernels will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-212058