An Algorithmic Framework for Sparse Bounded Component Analysis
Bounded component analysis (BCA) is a recent approach that enables the separation of both dependent and independent signals from their mixtures. This paper introduces a novel deterministic instantaneous BCA framework for the separation of sparse bounded sources. The framework is based on a geometric maximization setting, where the objective function is defined as the volume ratio of two objects, namely, the principal hyperellipsoid and the bounding $\ell _1$-norm ball, defined over the separator output samples. It is shown that all global maxima of this objective are perfect separators. This paper also provides the corresponding iterative algorithms for both real and complex sparse sources. The numerical experiments illustrate the potential benefits of the proposed approach, with applications on image separation and neuron identification.