Scale Recognition, Regularization Parameter Selection, and Meyer's G Norm in Total Variation Regularization

Source: UCLA CAM Report 05-02 2005;.
Author: Strong DM, Aujol J-F, Chan TF.

Abstract:
We investigate how TV regularization naturally recognizes scale of individual features of an image and we show how this perception of scale depends on the amount of regularization applied to the image We give an automatic method driven by the geometry of the image for nding the minimum value of the regularization parameter needed to remove all features below a userchosen threshold We explain the relation of Meyers G norm to the perception of scale which provides a more intuitive understanding of this norm We consider other applications of this ability to recognize scale including the multiscale eects of TV regularization and the rate of loss of image features of various scales as a function of increasing amounts of regularization Several numerical results are given