Struggling to isolate original sounds from a mixed recording? This paper introduces a two-stage process for blind source separation, a common problem in acoustics, radio, and medical signal processing, using sparse decomposition in a signal dictionary. The method addresses the challenge of extracting underlying source signals from linear mixtures where the mixing matrix is unknown. The process begins with the a priori selection of an overcomplete signal dictionary, such as a wavelet frame or learned dictionary, where sources are assumed to be sparsely representable. It's followed by unmixing the sources by exploiting their sparse representability. The research considers the general case of more sources than mixtures and offers a more efficient algorithm for nonovercomplete dictionaries with equal numbers of sources and mixtures. Experiments using artificial signals and musical sounds demonstrated separation significantly better than other known techniques. The model offers a viable and robust solution for enhancing signal fidelity in various applications, from music production to medical diagnostics.
Published in Neural Computation, this paper aligns with the journal's focus on computational and mathematical approaches to understanding neural and cognitive processes. The application of sparse decomposition techniques to the problem of blind source separation contributes to the broader field of signal processing and neural-inspired algorithms.