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vca.m
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vca.m
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function [Ae, indice, Rp, sigma2est] = vca(R,varargin)
% Vertex Component Analysis
%
% [Ae, indice, Rp] = vca(R,'Endmembers',p,'SNR',r,'verbose',v)
%
% ------- Input variables -------------
% R - matrix with dimensions L(channels) x N(pixels)
% each pixel is a linear mixture of p endmembers
% signatures R = M x s, where s = gamma x alfa
% gamma is a illumination perturbation factor and
% alfa are the abundance fractions of each endmember.
% 'Endmembers'
% p - positive integer number of endmembers in the scene
%
% ------- Output variables -----------
% A - estimated mixing matrix (endmembers signatures)
% indice - pixels that were chosen to be the most pure
% Rp - Data matrix R projected.
%
% ------- Optional parameters---------
% 'SNR'
% r - (double) signal to noise ratio (dB)
% 'verbose'
% v - [{'on'} | 'off']
% ------------------------------------
%
% Authors: José Nascimento (zen@isel.pt)
% José Bioucas Dias (bioucas@lx.it.pt)
% Copyright (c)
% version: 2.1 (7-May-2004)
%
% For any comment contact the authors
%
% more details on:
% José M. P. Nascimento and José M. B. Dias
% "Vertex Component Analysis: A Fast Algorithm to Unmix Hyperspectral Data"
% submited to IEEE Trans. Geosci. Remote Sensing, vol. .., no. .., pp. .-., 2004
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Default parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
verbose = 'on'; % default
snr_input = 0; % default this flag is zero,
% which means we estimate the SNR
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Looking for input parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
dim_in_par = length(varargin);
if (nargin - dim_in_par)~=1
error('Wrong parameters');
elseif rem(dim_in_par,2) == 1
error('Optional parameters should always go by pairs');
else
for i = 1 : 2 : (dim_in_par-1)
switch lower(varargin{i})
case 'verbose'
verbose = varargin{i+1};
case 'endmembers'
p = varargin{i+1};
case 'snr'
SNR = varargin{i+1};
snr_input = 1; % flag meaning that user gives SNR
otherwise
fprintf(1,'Unrecognized parameter:%s\n', varargin{i});
end %switch
end %for
end %if
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Initializations
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if isempty(R)
error('there is no data');
else
[L N]=size(R); % L number of bands (channels)
% N number of pixels (LxC)
end
if (p<0 | p>L | rem(p,1)~=0),
error('ENDMEMBER parameter must be integer between 1 and L');
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% SNR Estimates
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if snr_input==0,
r_m = mean(R,2);
R_m = repmat(r_m,[1 N]); % mean of each band
R_o = R - R_m; % data with zero-mean
[Ud,Sd,Vd] = svds(R_o*R_o'/N,p); % computes the p-projection matrix
x_p = Ud' * R_o; % project the zero-mean data onto p-subspace
[SNR sigma2est]= estimate_snr(R,r_m,x_p);
if strcmp (verbose, 'on'), fprintf(1,'SNR estimated = %g[dB]\n',SNR); end
else
if strcmp (verbose, 'on'), fprintf(1,'input SNR = %g[dB]\t',SNR); end
end
SNR_th = 15 + 10*log10(p);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Choosing Projective Projection or
% projection to p-1 subspace
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if SNR < SNR_th,
if strcmp (verbose, 'on'), fprintf(1,'... Select the projective proj.\n',SNR); end
d = p-1;
if snr_input==0, % it means that the projection is already computed
Ud= Ud(:,1:d);
else
r_m = mean(R,2);
R_m = repmat(r_m,[1 N]); % mean of each band
R_o = R - R_m; % data with zero-mean
[Ud,Sd,Vd] = svds(R_o*R_o'/N,d); % computes the p-projection matrix
x_p = Ud' * R_o; % project thezeros mean data onto p-subspace
end
Rp = Ud * x_p(1:d,:) + repmat(r_m,[1 N]); % again in dimension L
x = x_p(1:d,:); % x_p = Ud' * R_o; is on a p-dim subspace
c = max(sum(x.^2,1))^0.5;
y = [x ; c*ones(1,N)] ;
else
if strcmp (verbose, 'on'), fprintf(1,'... Select proj. to p-1\n',SNR); end
d = p;
[Ud,Sd,Vd] = svds(R*R'/N,d); % computes the p-projection matrix
x_p = Ud'*R;
Rp = Ud * x_p(1:d,:); % again in dimension L (note that x_p has no null mean)
x = Ud' * R;
u = mean(x,2); %equivalent to u = Ud' * r_m
y = x./ repmat( sum( x .* repmat(u,[1 N]) ) ,[d 1]);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% VCA algorithm
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
indice = zeros(1,p);
A = zeros(p,p);
A(p,1) = 1;
for i=1:p
w = rand(p,1);
f = w - A*pinv(A)*w;
f = f / sqrt(sum(f.^2));
v = f'*y;
[v_max indice(i)] = max(abs(v));
A(:,i) = y(:,indice(i)); % same as x(:,indice(i))
end
Ae = Rp(:,indice);
return;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% End of the vca function
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Internal functions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [snr_est sigma2est]= estimate_snr(R,r_m,x)
[L N]=size(R); % L number of bands (channels)
% N number of pixels (Lines x Columns)
[p N]=size(x); % p number of endmembers (reduced dimension)
P_y = sum(R(:).^2)/N;
P_x = sum(x(:).^2)/N + r_m'*r_m;
snr_est = 10*log10( (P_x - p/L*P_y)/(P_y- P_x) );
sigma2est = P_y- P_x;
return;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%