fpica.m

利用fastica数据包对给定的两幅混合图象利用独立成分分析进行分离。

      Xsub=X(:, getSamples(numSamples, sampleSize));
      B = (Xsub * (( Xsub' * B) .^ 3)) / size(Xsub,2) - 3 * B;
     case 13
      % Optimoitu
      Ysub=X(:, getSamples(numSamples, sampleSize))' * B;
      Gpow3 = Ysub .^ 3;
      Beta = sum(Ysub .* Gpow3);
      D = diag(1 ./ (Beta - 3 * size(Ysub', 2)));
      B = B + myy * B * (Ysub' * Gpow3 - diag(Beta)) * D;
      
      % tanh
     case 20
      hypTan = tanh(a1 * X' * B);
      B = X * hypTan / numSamples - ...
	  ones(size(B,1),1) * sum(1 - hypTan .^ 2) .* B / numSamples * ...
	  a1;
     case 21
      % optimoitu - epsilonin kokoisia 
      Y = X' * B;
      hypTan = tanh(a1 * Y);
      Beta = sum(Y .* hypTan);
      D = diag(1 ./ (Beta - a1 * sum(1 - hypTan .^ 2)));
      B = B + myy * B * (Y' * hypTan - diag(Beta)) * D;
     case 22
      Xsub=X(:, getSamples(numSamples, sampleSize));
      hypTan = tanh(a1 * Xsub' * B);
      B = Xsub * hypTan / size(Xsub, 2) - ...
	  ones(size(B,1),1) * sum(1 - hypTan .^ 2) .* B / size(Xsub, 2) * a1;
     case 23
      % Optimoitu
      Y = X(:, getSamples(numSamples, sampleSize))' * B;
      hypTan = tanh(a1 * Y);
      Beta = sum(Y .* hypTan);
      D = diag(1 ./ (Beta - a1 * sum(1 - hypTan .^ 2)));
      B = B + myy * B * (Y' * hypTan - diag(Beta)) * D;
      
      % gauss
     case 30
      U = X' * B;
      Usquared=U .^ 2;
      ex = exp(-a2 * Usquared / 2);
      gauss =  U .* ex;
      dGauss = (1 - a2 * Usquared) .*ex;
      B = X * gauss / numSamples - ...
	  ones(size(B,1),1) * sum(dGauss)...
	  .* B / numSamples ;
     case 31
      % optimoitu
      Y = X' * B;
      ex = exp(-a2 * (Y .^ 2) / 2);
      gauss = Y .* ex;
      Beta = sum(Y .* gauss);
      D = diag(1 ./ (Beta - sum((1 - a2 * (Y .^ 2)) .* ex)));
      B = B + myy * B * (Y' * gauss - diag(Beta)) * D;
     case 32
      Xsub=X(:, getSamples(numSamples, sampleSize));
      U = Xsub' * B;
      Usquared=U .^ 2;
      ex = exp(-a2 * Usquared / 2);
      gauss =  U .* ex;
      dGauss = (1 - a2 * Usquared) .*ex;
      B = Xsub * gauss / size(Xsub,2) - ...
	  ones(size(B,1),1) * sum(dGauss)...
	  .* B / size(Xsub,2) ;
     case 33
      % Optimoitu
      Y = X(:, getSamples(numSamples, sampleSize))' * B;
      ex = exp(-a2 * (Y .^ 2) / 2);
      gauss = Y .* ex;
      Beta = sum(Y .* gauss);
      D = diag(1 ./ (Beta - sum((1 - a2 * (Y .^ 2)) .* ex)));
      B = B + myy * B * (Y' * gauss - diag(Beta)) * D;
      
      % skew
     case 40
      B = (X * ((X' * B) .^ 2)) / numSamples;
     case 41
      % Optimoitu
      Y = X' * B;
      Gskew = Y .^ 2;
      Beta = sum(Y .* Gskew);
      D = diag(1 ./ (Beta));
      B = B + myy * B * (Y' * Gskew - diag(Beta)) * D;
     case 42
      Xsub=X(:, getSamples(numSamples, sampleSize));
      B = (Xsub * ((Xsub' * B) .^ 2)) / size(Xsub,2);
     case 43
      % Uusi optimoitu
      Y = X(:, getSamples(numSamples, sampleSize))' * B;
      Gskew = Y .^ 2;
      Beta = sum(Y .* Gskew);
      D = diag(1 ./ (Beta));
      B = B + myy * B * (Y' * Gskew - diag(Beta)) * D;

     otherwise
      error('Code for desired nonlinearity not found!');
    end
  end

  
  % Calculate ICA filters.
  W = B' * whiteningMatrix;
  
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  % Also plot the last one...
  switch usedDisplay
   case 1 
    % There was and may still be other displaymodes...
    % 1D signals
    icaplot('dispsig',(X'*B)');
    drawnow;
   case 2
    % ... and now there are :-)
    % 1D basis
    icaplot('dispsig',A');
    drawnow;
   case 3
    % ... and now there are :-)
    % 1D filters
    icaplot('dispsig',W);
    drawnow;
   otherwise
  end
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% DEFLATION APPROACH
if approachMode == 2
  
  B = zeros(vectorSize);
  
  % The search for a basis vector is repeated numOfIC times.
  round = 1;
  
  numFailures = 0;
  
  while round <= numOfIC,
    myy = myyOrig;
    usedNlinearity = gOrig;
    stroke = 0;
    notFine = 1;
    long = 0;
    endFinetuning = 0;
    
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    % Show the progress...
    if b_verbose, fprintf('IC %d ', round); end
    
    % Take a random initial vector of lenght 1 and orthogonalize it
    % with respect to the other vectors.
    if initialStateMode == 0
      w = rand(vectorSize, 1) - .5;
    elseif initialStateMode == 1
      w=whiteningMatrix*guess(:,round);
    end
    w = w - B * B' * w;
    w = w / norm(w);
    
    wOld = zeros(size(w));
    wOld2 = zeros(size(w));
    
    % This is the actual fixed-point iteration loop.
    %    for i = 1 : maxNumIterations + 1
    i = 1;
    gabba = 1;
    while i <= maxNumIterations + gabba
      if (usedDisplay > 0)
	drawnow;
      end
      if (interruptible & g_FastICA_interrupt)
        if b_verbose 
          fprintf('\n\nCalculation interrupted by the user\n');
        end
        return;
      end
      
      % Project the vector into the space orthogonal to the space
      % spanned by the earlier found basis vectors. Note that we can do
      % the projection with matrix B, since the zero entries do not
      % contribute to the projection.
      w = w - B * B' * w;
      w = w / norm(w);
      
      if notFine
	if i == maxNumIterations + 1
	  if b_verbose
	    fprintf('\nComponent number %d did not converge in %d iterations.\n', round, maxNumIterations);
	  end
	  round = round - 1;
	  numFailures = numFailures + 1;
	  if numFailures > failureLimit
	    if b_verbose
	      fprintf('Too many failures to converge (%d). Giving up.\n', numFailures);
	    end
	    if round == 0
	      A=[];
	      W=[];
	    end
	    return;
	  end
	  % numFailures > failurelimit
	  break;
	end
	% i == maxNumIterations + 1
      else
	% if notFine
	if i >= endFinetuning
	  wOld = w; % So the algorithm will stop on the next test...
	end
      end
      % if notFine
      
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      % Show the progress...
      if b_verbose, fprintf('.'); end;
      
      
      % Test for termination condition. Note that the algorithm has
      % converged if the direction of w and wOld is the same, this
      % is why we test the two cases.
      if norm(w - wOld) < epsilon | norm(w + wOld) < epsilon
        if finetuningEnabled & notFine
          if b_verbose, fprintf('Initial convergence, fine-tuning: '); end;
          notFine = 0;
	  gabba = maxFinetune;
          wOld = zeros(size(w));
          wOld2 = zeros(size(w));
          usedNlinearity = gFine;
          myy = myyK * myyOrig;
	  
	  endFinetuning = maxFinetune + i;
	  
        else
          numFailures = 0;
          % Save the vector
          B(:, round) = w;
	  
          % Calculate the de-whitened vector.
          A(:,round) = dewhiteningMatrix * w;
          % Calculate ICA filter.
          W(round,:) = w' * whiteningMatrix;
	  
          %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
          % Show the progress...
          if b_verbose, fprintf('computed ( %d steps ) \n', i); end
	  
          %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
          % Also plot the current state...
          switch usedDisplay
	   case 1
	    if rem(round, displayInterval) == 0,
	      % There was and may still be other displaymodes...   
	      % 1D signals
	      temp = X'*B;
	      icaplot('dispsig',temp(:,1:numOfIC)');
	      drawnow;
	    end
	   case 2
	    if rem(round, displayInterval) == 0,
	      % ... and now there are :-) 
	      % 1D basis
	      icaplot('dispsig',A');
	      drawnow;
	    end
	   case 3
	    if rem(round, displayInterval) == 0,
	      % ... and now there are :-) 
	      % 1D filters
	      icaplot('dispsig',W);
	      drawnow;
	    end
          end
	  % switch usedDisplay
	  break; % IC ready - next...
        end
	%if finetuningEnabled & notFine
      elseif stabilizationEnabled
	if (~stroke) & (norm(w - wOld2) < epsilon | norm(w + wOld2) < ...
			epsilon)
	  stroke = myy;
	  if b_verbose, fprintf('Stroke!'); end;
	  myy = .5*myy;
	  if mod(usedNlinearity,2) == 0
	    usedNlinearity = usedNlinearity + 1;
	  end
	elseif stroke
	  myy = stroke;
	  stroke = 0;
	  if (myy == 1) & (mod(usedNlinearity,2) ~= 0)
	    usedNlinearity = usedNlinearity - 1;
	  end
	elseif (notFine) & (~long) & (i > maxNumIterations / 2)
	  if b_verbose, fprintf('Taking long (reducing step size) '); end;
	  long = 1;
	  myy = .5*myy;
	  if mod(usedNlinearity,2) == 0
	    usedNlinearity = usedNlinearity + 1;
	  end
	end
      end
      
      wOld2 = wOld;
      wOld = w;
      
      switch usedNlinearity
	% pow3
       case 10
	w = (X * ((X' * w) .^ 3)) / numSamples - 3 * w;
       case 11
	EXGpow3 = (X * ((X' * w) .^ 3)) / numSamples;
	Beta = w' * EXGpow3;
	w = w - myy * (EXGpow3 - Beta * w) / (3 - Beta);
       case 12
	Xsub=X(:,getSamples(numSamples, sampleSize));
	w = (Xsub * ((Xsub' * w) .^ 3)) / size(Xsub, 2) - 3 * w;
       case 13
	Xsub=X(:,getSamples(numSamples, sampleSize));
	EXGpow3 = (Xsub * ((Xsub' * w) .^ 3)) / size(Xsub, 2);
	Beta = w' * EXGpow3;
	w = w - myy * (EXGpow3 - Beta * w) / (3 - Beta);
	% tanh
       case 20
	hypTan = tanh(a1 * X' * w);
	w = (X * hypTan - a1 * sum(1 - hypTan .^ 2)' * w) / numSamples;
       case 21
	hypTan = tanh(a1 * X' * w);
	Beta = w' * X * hypTan;
	w = w - myy * ((X * hypTan - Beta * w) / ...
		       (a1 * sum((1-hypTan .^2)') - Beta));
       case 22
	Xsub=X(:,getSamples(numSamples, sampleSize));
	hypTan = tanh(a1 * Xsub' * w);
	w = (Xsub * hypTan - a1 * sum(1 - hypTan .^ 2)' * w) / size(Xsub, 2);
       case 23
	Xsub=X(:,getSamples(numSamples, sampleSize));
	hypTan = tanh(a1 * Xsub' * w);
	Beta = w' * Xsub * hypTan;
	w = w - myy * ((Xsub * hypTan - Beta * w) / ...
		       (a1 * sum((1-hypTan .^2)') - Beta));
	% gauss
       case 30
	% This has been split for performance reasons.
	u = X' * w;
	u2=u.^2;
	ex=exp(-a2 * u2/2);
	gauss =  u.*ex;
	dGauss = (1 - a2 * u2) .*ex;
	w = (X * gauss - sum(dGauss)' * w) / numSamples;
       case 31
	u = X' * w;
	u2=u.^2;
	ex=exp(-a2 * u2/2);
	gauss =  u.*ex;
	dGauss = (1 - a2 * u2) .*ex;
	Beta = w' * X * gauss;
	w = w - myy * ((X * gauss - Beta * w) / ...
		       (sum(dGauss)' - Beta));
       case 32
	Xsub=X(:,getSamples(numSamples, sampleSize));
	u = Xsub' * w;
	u2=u.^2;
	ex=exp(-a2 * u2/2);
	gauss =  u.*ex;
	dGauss = (1 - a2 * u2) .*ex;
	w = (Xsub * gauss - sum(dGauss)' * w) / size(Xsub, 2);
       case 33
	Xsub=X(:,getSamples(numSamples, sampleSize));
	u = Xsub' * w;
	u2=u.^2;
	ex=exp(-a2 * u2/2);
	gauss =  u.*ex;
	dGauss = (1 - a2 * u2) .*ex;
	Beta = w' * Xsub * gauss;
	w = w - myy * ((Xsub * gauss - Beta * w) / ...
		       (sum(dGauss)' - Beta));
	% skew
       case 40
	w = (X * ((X' * w) .^ 2)) / numSamples;
       case 41
	EXGskew = (X * ((X' * w) .^ 2)) / numSamples;
	Beta = w' * EXGskew;
	w = w - myy * (EXGskew - Beta*w)/(-Beta);
       case 42
	Xsub=X(:,getSamples(numSamples, sampleSize));
	w = (Xsub * ((Xsub' * w) .^ 2)) / size(Xsub, 2);
       case 43
	Xsub=X(:,getSamples(numSamples, sampleSize));
	EXGskew = (Xsub * ((Xsub' * w) .^ 2)) / size(Xsub, 2);
	Beta = w' * EXGskew;
	w = w - myy * (EXGskew - Beta*w)/(-Beta);
	
       otherwise
	error('Code for desired nonlinearity not found!');
      end
      
      % Normalize the new w.
      w = w / norm(w);
      i = i + 1;
    end
    round = round + 1;
  end
  if b_verbose, fprintf('Done.\n'); end
  
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  % Also plot the ones that may not have been plotted.
  if (usedDisplay > 0) & (rem(round-1, displayInterval) ~= 0)
    switch usedDisplay
     case 1
      % There was and may still be other displaymodes...
      % 1D signals
      temp = X'*B;
      icaplot('dispsig',temp(:,1:numOfIC)');
      drawnow;
     case 2
      % ... and now there are :-)
      % 1D basis
      icaplot('dispsig',A');
      drawnow;
     case 3
      % ... and now there are :-)
      % 1D filters
      icaplot('dispsig',W);
      drawnow;
     otherwise
    end
  end
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% In the end let's check the data for some security
if ~isreal(A)
  if b_verbose, fprintf('Warning: removing the imaginary part from the result.\n'); end
  A = real(A);
  W = real(W);
end




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% Subfunction
% Calculates tanh simplier and faster than Matlab tanh.
function y=tanh(x)
y = 1 - 2 ./ (exp(2 * x) + 1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function Samples = getSamples(max, percentage)
Samples = find(rand(1, max) < percentage);