A regularized optimization approach for AM-FM reconstructions

The AM-FM Dominant and Channelized Component Analysis (DCA and CCA respectively), consist of applying a filter bank to the Hilbert-tranformed image, and then proceeding with the AM-FM demodulation of each band-pass filtered image. Whereas AM-FM reconstructions based on the CCA use a reasonably small number of locally coherent components, those based on the DCA only use one component: the estimates from the channel with the maximum amplitude estimate. Both types of reconstructions are known to produce noticeable visual artifacts. We propose a method, based on a regularized optimization of the estimates from the CCA, which attains a small number of locally coherent components and simultaneously enforces a piecewise smooth constrain for the amplitude functions. Moreover, this method offers high quality reconstructions when compared to standard CCA and DCA reconstructions and state of the art techniques.