Fast Cartoon + Texture Image Filters

Abstract--Can images be decomposed into the sum of a geometric part and a textural part? In a theoretical breakthrough, [Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations. Providence, RI: American Mathematical Society, 2001] proposed variational models that force the geometric part into the space of functions with bounded variation, and the textural part into a space of oscillatory distributions. Meyer's models are simple minimization problems extending the famous total variation model. However, their numerical solution has proved challenging. It is the object of a literature rich in variants and numerical attempts. This paper starts with the linear model, which reduces to a low-pass/high-pass filter pair. A simple conversion of the linear filter pair into a nonlinear filter pair involving the total variation is introduced. This new-proposed nonlinear filter pair retains both the essential features of Meyer's models and the simplicity and ra...

• Type: Journal
• Year: 2010
• Where: TIP
• Authors: Antoni Buades, Triet M. Le, Jean-Michel Morel, Luminita A. Vese
• Keywords: Education, Filter Pair, Nonlinear Filter Pair, TIP 2010, Total Variation