Bounded Component Analysis of linear mixtures

The blind decomposition of the observations, as a set of additive components of simpler structure, is a problem with many applications in scientific and practical fields. Our study assumes that the component signals are of bounded nature, and relies on the geometric decomposition of the convex set that supports the observations as a Minkowski direct sum of the convex sets that support the components. This last property, which is weaker than the mutual independence of the additive components of the observations, is sufficient for the essential identifiability of the bounded and indecomposable components. In practice, it is usual that the components lie in one-dimensional complex subspaces. Therefore, for this case, we describe a sequential method for their recovery.