Compressed data separation via unconstrained l(1)-split analysis

We investigate the problems of reconstruction signals' distinct subcomponents, that. are approximately sparse in terms of morphologically different dictionaries, from a few noisy linear measurements. We show that under common assumptions on a restricted isometric property adapted to the composed dictionary and a mutual coherence condition between the two different dictionaries, the two distinct subcomponents can be stably and approximately recovered via the unconstrained l(1)-split analysis, with an error bound that is in general unimprovable for the Gaussian noises.