l21_bss08

l21_bss08 - MIT OpenCourseWare http:/ocw.mit.edu HST.582J /...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
MIT OpenCourseWare http://ocw.mit.edu HST.582J / 6.555J / 16.456J Biomedical Signal and Image Processing Spring 2007 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
HST.582J/6.555J/16.456J Gari D. Clifford http://www.mit.edu/~gari © G. D. Clifford 2005-2008 Blind Source Separation: PCA & ICA Cite as: Gari Clifford. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. Harvard-MIT Division of Health Sciences and Technology HST.582J: Biomedical Signal and Image Processing, Spring 2007 Course Director: Dr. Julie Greenberg
Background image of page 2
What is BSS? Assume an observation (signal) is a linear mix of >1 unknown independent source signals The mixing (not the signals) is stationary We have as many observations as unknown sources To find sources in observations - need to define a suitable measure of independence … For example - the cocktail party problem (sources are speakers and background noise): Cite as: Gari Clifford. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The cocktail party problem - find Z A z 1 z 2 z N X T Z T X T = AZ T x 1 x 2 x N Cite as: Gari Clifford. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
Background image of page 4
Formal statement of problem N independent sources … Z mn ( M x N ) • linear square mixing A nn ( N x N ) (#sources=#sensors) • produces a set of observations … X mn ( M x N ) ….. X T = AZ T Cite as: Gari Clifford. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Formal statement of solution • ‘demix’ observations … X T ( N x M ) into Y T = WX T Y T ( N x M ) Z T W ( N x N ) A -1 How do we recover the independent sources? ( We are trying to estimate W A -1 ) …. We require a measure of independence ! Cite as: Gari Clifford. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
Background image of page 6
‘Signal’ source ‘Noise’ sources Z T Observed mixtures X T = AZ T Y T = WX T Cite as: Gari Clifford. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. POLICE POLICE Figure s by MIT OpenCourseWare.
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
X T = A Z T Y T = W X T T T TT Cite as: Gari Clifford. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007.
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 64

l21_bss08 - MIT OpenCourseWare http:/ocw.mit.edu HST.582J /...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online