CS134 Project Milestone

Audio Source Separation

My email: Xiaoyu.Zhao@dartmouth.edu

Fast ICA algorithm summary:

  • Principle: The distribution of a sum of independent variables is more gaussian distributed than any one of the components. When taking a vector w which maximizes the nongaussiananity of w^Tx, w^Tx equals one of the independent components. y=W^Tx=W^TAs
  • Measurement of Nongaussianity: approximation of negentropy J(y) oc [E{G(y)}-E{G(v)}]^2, G(u)=1/a1(log cosh a1*u), or G(u)=-exp(-u^2/2)
  • Fast ICA algo for one unit:
        1.Initialize W
       Repeat from step2 until convergence
         1.W^+=E{xg(W^Tx)}-E{g'(W^Tx)}W
         2.Normalize on w
  • Fast ICA for several units(deflation)
       1.Give the units a weight vector w1,...,wn
       loop p=1:n
         1.wp+1 = wp+1-sum(i=1:p)wp+1^Twjwj
         2.normalize wp+1

    • Progress

    Finished:
    Coding for centering, whitenning(reduces the dimension of parameters to be estimated)
    Ongoing:
    Debugging fast ICA algo.
    visualizations of whitening:[mix][afterWhitening]

    Dataset:

  • Standard Matlab sound files (handel, chirp, gong)
  • Sound track from website: http://www.dcs.warwick.ac.uk/~yu/[mix1][mix2][mix3][mix4]
  • Image dataset comes from http://www.cis.hut.fi/projects/ica/data/images/

    • Reference

  • Aapo Hyvarinen and Erkki Oja, Neural Networks Research Center Helsinki University of Technology, Independent Component Analysis: Algorithm and Applications.
  • Hiroshi Saruwatari , Blind Source Separation Combining Independent Component Analysis and Beamforming
  • H.Farid E.H.Adelson, Separating reflections from images by use of independent component analysis. Jornal of the optical society of america. 16(9):2136-2145, 1999