Blind Source Separation

When all the sources of the signals and also the mixing methodology is completely unknown, the Blind source separation technique comes into consideration. From the name, we can understand it separates signals ‘blindly’ i.e. maximum numbers are not known of the mixed signals but we need to separate them. In real life, there are many situations where it is necessary to separate the mixed signal into it’s each signal. Also, there is a high possibility that the mixed signal contains noises. Blind Source Separation is used to handle these types of situations where separation is important but most things are not known about its input signal.

Application of Blind Source Separation: 

 It is used in many domains like Audio source separation(speech separation and music industry), Medical tests(electroencephalography, Magnetic Resonance Imaging(MRI), electrocardiography, etc.), and communication applications. 

FastICA is the most popular method and the fastest algorithm to perform Independent Component Analysis. It can be used to separate all the individual signals from a mixed signal. 

Independent Component Analysis(ICA) is a method where it performs a search for finding mutually independent non-Gaussian latent variables. Here, the components of the multivariate data are assumed to be linear combinations of them. 

 FastICA is of two types.

1. Deflation-based FastICA where the components are found in one by one manner.
2. Symmetric FastICA where the components are found simultaneously. 

FastICA has some prominent features it can use any nonlinearity function and optimizes the extraction order in the deflation-based version.  

Mathematical Approach  

FastICA can be used to separate all the individual signals from a mixed signal. So let us assume a set of individual source signals is  where . These signal can be mixed using a matrix . After mixing the signal it produces a mixed signal . 

• Generally . 
• If n " title="Rendered by QuickLaTeX.com" height="17" width="73" style="vertical-align: -2px;">, then the system of equations is overdetermined and the conventional linear method is used to unmix the signals. 
• If m " title="Rendered by QuickLaTeX.com" height="17" width="74" style="vertical-align: -2px;">, then a non-linear method must be implemented because the system performs underdetermined. 

Now FastICA algorithm is used to unmix these signals as there are some multidimensional signals that can be present on the mixed signals. Blind source separation can effectively unmix these signals with the help of the FastICA algorithm by determining an un-mixing matrix   Then it recovers the approximation of the original signals,

We will see the steps of FastICA algorithms later on in this article. 

Applications of FastICA

FastICA is used in various fields in real-life events like a mixed sound wave from multiple independent sources we can easily find out each signal wave along with its source by using FastICA. Also let if a room is full of people and there are a certain number of microphones, we can use FastICA to identify everyone from the mixed sound waves captures by microphones.