Restricted q-Isometry properties adapted to frames for nonconvex l_q -analysis

This paper discusses the reconstruction of signals from few measurements in the situation that signals are sparse or approximately sparse in terms of a general frame via the l_q -analysis optimization with 0q -analysis optimization. We then determine how many random Gaussian measurements are needed for the condition to hold with high probability. The resulting sufficient condition is met by fewer measurements for smaller q than when q=1. The introduced generalized q -RIP is also useful in compressed data separation. In compressed data separation, one considers the problem of reconstruction of signals' distinct subcomponents, which are (approximately) sparse in morphologically different dictionaries, from few measurements. With the notion of generalized q -RIP, we show that under a usual assumption that the dictionaries satisfy a mutual coherence condition, the l_q split analysis with 0