Projection Design for Compressive Source Separation Using Mean Errors and Cross-Validation

This paper addresses the task of projection design for source separation in the compressive domain, where one observes a compressed linear mixture of two source signals with known priors. By positioning that both the sources follow a Gaussian mixture, we formulate an objective that tightly approximates the minimum mean squared error and solve the optimization problem using a gradient-based approach. In the blind setting, where the mixing ratio unknown, we propose a cross-validation approach to independently estimate the mixing ratio. We also provide a number of numerical results on synthetic and real image data that validate our findings. To the best of our knowledge, this is the first effort in projection design for prior-based source separation.