Blind signal separation

Blind signal separation (BSS), also known as blind source separation, is the separation of a set of source signals from a set of mixed signals, without the aid of information (or with very little information) about the source signals or the mixing process. This problem is in general highly underdetermined, but useful solutions can be derived under a surprising variety of conditions. Much of the early literature in this field focuses on the separation of temporal signals such as audio. However, blind signal separation is now routinely performed on multidimensional data, such as images and tensors, which may involve no time dimension whatsoever.

The set of individual source signals, ${\displaystyle s(t)=(s_{1}(t),\dots ,s_{n}(t))^{T}}$, is 'mixed' using a matrix, ${\displaystyle A=[a_{ij}]\in \mathbb {R} ^{m\times n}}$, to produce a set of 'mixed' signals, ${\displaystyle x(t)=(x_{1}(t),\dots ,x_{m}(t))^{T}}$, as follows. Usually, ${\displaystyle n}$ is equal to ${\displaystyle m}$. If ${\displaystyle m>n}$, then the system of equations is overdetermined and thus can be unmixed using a conventional linear method. If ${\displaystyle n>m}$, the system is underdetermined and a non-linear method must be employed to recover the unmixed signals. The signals themselves can be multidimensional.

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