Report on the Total Variation Spectral Framework

G. Gilboa, “A Total Variation Spectral Framework for Scale and Texture Analysis”, CCIT Report 833, 2013.


A new total variation (TV) spectral framework is presented. A TV transform is proposed which can be interpreted as a spectral domain, where elementary TV features, like disks, approach impulses. A reconstruction formula from the pectral to the spatial domain is given, allowing the design of new filters.The framework allows deeper understanding of scales in an $L^1$ sense and the ability to better analyze and process textures. An example of a texture processing application illustrates possible benefits of this new framework.