Sourceseparation

Sourceseparation, also known as source separation, is the set of techniques for recovering individual source signals from observed mixtures, without (or with limited) knowledge of the mixing process. It is a central problem in signal processing, with broad applications across audio, image, and biomedical domains. In audio, the goal is often to separate concurrent sound sources, such as voices and instruments, from a recording captured by microphones or a single-channel track. The problem can be categorized as determined, underdetermined, or overdetermined depending on the number of sources relative to sensors.

Two broad modes exist: blind sourceseparation, where little is assumed about the sources or the mixer, and informed or semi-supervised approaches that use partial information. Classical methods include Independent Component Analysis, which seeks statistically independent components; and Nonnegative Matrix Factorization, which decomposes magnitude spectrograms into libraries of spectral templates. In audio, beamforming exploits spatial structure from microphone arrays. Modern approaches increasingly rely on deep learning, using models that map mixtures to source estimates, such as time-domain networks and spectrogram-based networks trained on large paired datasets.

Applications include speech enhancement, vocal separation in music production, and noise suppression in hearing aids. Evaluation uses objective measures such as source-to-distortion ratio, source-to-interference ratio, and perceptual metrics; the BSS Eval toolkit is commonly used.

Challenges include reverberation, noise, permutation ambiguity, and scaling ambiguity, especially in blind settings. When the number of sources exceeds the number of microphones (underdetermined), separation is particularly difficult. Generalization across speakers, accents, and environments remains an active area.