subback (Spectra, xaxis, iter, order, doplot)

%function subback
%
%This function will subtract the background of a spectrum in a iterative
%way. It will fit a polynom through the datapoints and those points either
%of the fitted polynome or those of the spectrum below the fitted spectrum
%will be used for the following iteration. In this way, with higher
%iterations, one obtains a better prediction of the background.
%
%Syntax:
%    NewSpectra = subback (Spectra, xaxis, iter, order, doplot)
%    NewSpectra = subback (Spectra, xaxis)
%
%With:
%    Spectra: datamatrix with the spectra in rows
%    xaxis: the corresponding x-axis
%    iter: the number of iterations to do, standard value 200
%    order: order of the polynom used for fitting, standard value 5
%    doplot: boolean: indicates whether plots of the original spectrum with
%        fitted background, and plots of the resulting spectrum need to be
%        made
%    NewSpectra: the spectra with the background subtracted
%
%Literature:
%    1) Lieber CA, Mahadevan-Jansen A, Automated method for subtraction of
%    fluorescence from biological Raman spectra, Applied spectroscopy, 57
%    (2003) 11, 1363-1367
%
%Example:
%    load data
%    xaxis = 1:size(data,2);
%    subplot (2,1,1);
%    plot (xaxis, data);
%    title ('Original dataset');
%    subplot (2, 1, 2);
%    plot (xaxis, subback (data, xaxis, 100, 5, 0));
%    title ('Background subtracted');

%The Biodata toolbox for MATLAB: a spectral database system for storing and
%processing spectra
%C 2005-2008, Kris De Gussem, Raman Spectroscopy Research Group, Department
%of analytical chemistry, Ghent University
%C 2009 Kris De Gussem
%
%This file is part of Biodata.
%
%Biodata is free software: you can redistribute it and/or modify
%it under the terms of the GNU General Public License as published by
%the Free Software Foundation, either version 3 of the License, or
%(at your option) any later version.
%
%Biodata is distributed in the hope that it will be useful,
%but WITHOUT ANY WARRANTY; without even the implied warranty of
%MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%GNU General Public License for more details.
%
%You should have received a copy of the GNU General Public License
%along with Biodata.  If not, see <http://www.gnu.org/licenses/>.

%Copyright (c) 2005-2009, Kris De Gussem
%All rights reserved.
%
%Redistribution and use in source and binary forms, with or without 
%modification, are permitted provided that the following conditions are 
%met:
%
%    * Redistributions of source code must retain the above copyright 
%      notice, this list of conditions and the following disclaimer.
%    * Redistributions in binary form must reproduce the above copyright 
%      notice, this list of conditions and the following disclaimer in 
%      the documentation and/or other materials provided with the distribution
%    * Neither the name of Raman Spectroscopy Research Group, Department of
%	  analytical chemistry, Ghent University nor the names 
%      of its contributors may be used to endorse or promote products derived 
%      from this software without specific prior written permission.
%      
%THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 
%AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 
%IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 
%ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 
%LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 
%CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 
%SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 
%INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 
%CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 
%ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 
%POSSIBILITY OF SUCH DAMAGE.

function [NewSpectra, param] = subback (Spectra, xaxis, iter, order, doplot)
switch nargin
    case 2
        doplot = 0;
        iter = 200;
        order = 5;
    case 5
    otherwise
        error ('Biodata:msg', 'Wrong number of input parameters...');
end

[m,n] = size(Spectra);
NewSpectra = zeros(m,n);
warning off MATLAB:polyfit:RepeatedPointsOrRescale
param.P = cell(m,1);
param.S = cell(m,1);

h_importspec = waitbar(0,'Subtracting background...');
for nr = 1:m %do all spectra in matrix
    waitbar(nr/m, h_importspec);
    
    ThisSpectrum = Spectra(nr,:);
    for i = 1:iter %just do some iterations so that iwhe have a perfect estimate of the background
        [P,S] = polyfit(xaxis,ThisSpectrum,order);
        NewSpectra(nr,:) = polyval (P, xaxis);
        ind = find (NewSpectra(nr,:) > ThisSpectrum);
        NewSpectra(nr,ind) = ThisSpectrum(1,ind);
        ThisSpectrum = NewSpectra(nr,:);
    end
    back = polyval (P, xaxis);
    
    if doplot
        %plot the two spectra
        figure('name', 'Result of background subtraction');
        plot (xaxis, Spectra(nr,:), 'b',xaxis, NewSpectra(nr,:), 'r');
        h = title ([ 'Spectrum ' num2str(nr) ]);
        set(h, 'Fontweight', 'bold');
        set(h, 'Fontsize', 16);
        legend('Original spectrum', 'Fitted background');
        figure('name', 'Result: background-subtracted spectrum');
        
        %plot the final spectrum as wel
        plot (xaxis, Spectra(nr,:)-back);
        h = title ([ 'Spectrum ' num2str(nr) ]);
        set(h, 'Fontweight', 'bold');
        set(h, 'Fontsize', 16);
    end
    NewSpectra(nr,:) = Spectra(nr,:)-back;
    try
        param.P{nr} = P;
        param.S{nr} = S;
    catch
    end
end
close(h_importspec);
warning on MATLAB:polyfit:RepeatedPointsOrRescale

param.iter = iter;
param.order = order;
param.doplot = doplot;