A flatness based recovery algorithm for sparse multiband signals without number of bands prior

This paper presents a flatness based simultaneous orthogonal matching pursuit algorithm (SOMP) for the reconstruction of sparse multiband signals in the framework of modulated wideband converter (MWC). Compared with standard SOMP algorithm, the most innovation of this algorithm is that there is no prior knowledge assumed on the number of active bands. In the standard SOMP algorithm, the solution is guaranteed within k iterations, where k is the number of active bands. When k is not known in advance, sparsity adaptive matching pursuit (SAMP) proposed for single measurement vector problems can be easily extended for the reconstruction of sparse multiband signals, unfortunately with the drawback of high complexity. SAMP is inherently a kind of combinational method. Theoretical analysis demonstrates that the residual is monotonous and eventually converges to zero. For exactly sparse signals, in the case of measurement noise free, there is a sharp edge after k iterations. We demonstrate that the position of the sharp edge can be estimated by carefully checking its flatness. Simulation results demonstrate that the proposed algorithm outperforms the standard SOMP with comparable complexity.