Blind Source Separation of Compressively Sensed Signals

We present an approach to simultaneously separate and reconstruct signals from a compressively sensed linear mixture. We assume that the signals have a common sparse representation. The approach combines classical Compressive Sensing (CS) theory with a linear mixing model. Since Blind Source Separation (BSS) from a linear mixture is only possible up to permutation and scaling, factoring out these ambiguities leads to the problem of `1-minimization over the so-called oblique manifold. We discuss the occurring cost function and propose a geometric conjugate subgradient method to solve the problem.