G. Gilboa, “A spectral approach to total variation”, Scale-Space and Variational Methods, SSVM 2013, LNCS 7893, p. 36-47, 2013.
The total variation (TV) functional is explored from a spectral perspective. We formulate a TV transform based on the second time derivative of the total variation flow, scaled by time. In the transformation domain disks yield impulse responses. This transformation can be viewed as a spectral domain, with somewhat similar intuition of classical Fourier analysis. A simple reconstruction formula from the TV spectral domain to the spatial domain is given. We can then design low-pass, high-pass and band-pass TV filters and obtain a TV spectrum of signals and images.