Multichannel blind compressed sensing

Compressed sensing successfully recovers a signal, which is sparse under some basis representation, from a small number of linear measurements. However, prior knowledge of the sparsity basis is essential for the recovery process. The purpose of blind compressed sensing is to avoid the need for this prior knowledge. We consider blind compressed sensing in multichannel systems, in which the sparsity basis is unknown in both the sampling and recovery stages. Blind compressed sensing is achieved by simultaneously measuring several signals. We then suggest a simple algorithm to retrieve the unknown input. Under conditions presented in this work we demonstrate that our method can achieve results similar to those of standard compressed sensing, which rely on prior knowledge of the sparsity basis.