function [dat, w] = ft_preproc_denoise(dat, refdat, hilbertflag)

% FT_PREPROC_DENOISE performs a regression of the matrix dat onto refdat, and

% subtracts the projected data. This is for the purpose of removing signals generated

% by coils during continuous head motion tracking, for example.

%

% Use as

% [dat] = ft_preproc_denoise(dat, refdat, hilbertflag)

% where

% dat data matrix (Nchan1 X Ntime)

% refdat data matrix (Nchan2 X Ntime)

% hilbertflag boolean, regress out the real and imaginary parts of the Hilbert

% transformed signal, this is only meaningful for narrow band

% reference data (default = false)

%

% The number of channels of the data and reference data does not have to be the same.

%

% If the data contains NaNs, the output of the affected channel(s) will be all NaN.

%

% See also PREPROC

% Copyright (C) 2009, Jan-Mathijs Schoffelen

%

% This file is part of FieldTrip, see http://www.fieldtriptoolbox.org

% for the documentation and details.

%

% FieldTrip 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.

%

% FieldTrip 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 FieldTrip. If not, see <http://www.gnu.org/licenses/>.

%

% $Id$

if nargin<3

hilbertflag = 0;

end

% preprocessing fails on channels that contain NaN

if any(isnan(dat(:))) || any(isnan(refdat(:)))

ft_warning('FieldTrip:dataContainsNaN', 'data contains NaN values');

end

n1 = size(dat,2);

n2 = size(refdat,2);

m1 = nanmean(dat,2);

m2 = nanmean(refdat,2);

%remove mean

refdat = refdat-m2(:,ones(n2,1));

tmpdat = dat-m1(:,ones(n1,1));

%do hilbert transformation

if hilbertflag>0

hrefdat = hilbert(refdat')';

refdat = [real(hrefdat);imag(hrefdat)];

end

c12 = tmpdat*refdat'; %covariance between signals and references

c1 = refdat*refdat'; %covariance between references and references

w = (pinv(c1)*c12')'; %regression weights

%subtract

dat = dat-w*refdat;