Analog to Information conversion is a new paradigm in signal digitalization. In this framework, compressed sensing theory allows to reconstruct sparse signal from a limited number of measures. In this work, we will assume that the signal is not only sparse but also localized in a given domain, so that its energy is concentrated in a subspace. We will present a formal and quantitative discussion to explain how localization of sparse signals can be exploited to improve the quality of the reconstructed signal.