Joint blind source separation and declipping: a geometric approach for time disjoint sources

Source separation remains a challenging problem, made even more challenging when the mixtures are distorted. We present a novel framework for the source separation from mixtures affected by clipping distortion. Our method combines ℓ₁ minimization with knowledge about the geometry of clipped mixtures when the sources are disjoint in time. Our algorithm recovers the sources by solving a convex optimization problem, which is constrained by the clipping geometry. Comparative evaluation experiments show a significant increase in objective recovery performance of our proposed joint method compared to sequential approaches for speech and synthetic signals.