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# Application of Information Theory to Blind Source Separation

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Introduction   ::   BSS   ::   Mackay's Approach   ::   Natural Gradient   ::   p(u)

## Mackay's approach

We consider the BSS problem as a ML estimation problem. To begin with, we state a lemma that we will need.

Given a sequence of observed data obtained from we write down the joint probability as

To do ML estimation of A we examine

The ML solution is to find the A that maximizes this likelihood function. We have

where the lemma we derived before has been used. The log likelihood function is

Let W = A -1 . Then

Now we proceed as before, computing the derivative of the log likelihood with respect to W . The first part is easy:

For the first part:

Let

and let . Then we have

Thus

Compare with what we had before!

Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, May 17). Application of Information Theory to Blind Source Separation. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Information_Theory/lecture4_3.htm. This work is licensed under a Creative Commons License