Structured dictionary optimization: application to the modulated wideband converter

We consider the Modulated Wideband Converter (MWC) architecture [3] that aims at sub-Nyquist reconstruction of sparse wideband signals. The goal of this paper is to optimize the selection of the periodic sequences which are used to alias the spectrum of the input signal. In particular, we consider here the specific setting when the filter cutoff and sampling frequency is increased in order to obtain multiple mixtures of the aliased subbands in each physical channel. This setting implies a structured dictionary yielding a challenging optimization problem which has not been covered in the literature. We propose and extend methods based on $\ell_{2}$ and $\ell_{\infty}$ norms minimization to solve this particular problem.