Introduction
When the independence assumption is correct, blind ICA separation of a mixed signal gives very good results. It is also used for signals that are not supposed to be generated by a mixing for analysis purposes. A simple application of ICA is the "cocktail party problem", where the underlying speech signals are separated from a sample data consisting of people talking simultaneously in a room. Usually the problem is simplified by assuming no time delays or echoes. An important note to consider is that if N sources are present, at least N observations (e.g. microphones) are needed to get the original signals. This constitutes the square case (J = D, where D is the input dimension of the data and J is the dimension of the model). Other cases of underdetermined (J < D) and overdetermined (J > D) have been investigated.
Read more about this topic: Independent Component Analysis
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