qrs_detect2.m

function [qrs_pos,sign,en_thres] = qrs_detect2(ecg,varargin)
% QRS detector based on the P&T method. This is an offline implementation
% of the detector.
%
% inputs
%   ecg:            one ecg channel on which to run the detector (required)
%                   in [mV]
%   varargin
%       THRES:      energy threshold of the detector (default: 0.6) 
%                   [arbitrary units]
%       REF_PERIOD: refractory period in sec between two R-peaks (default: 0.250)
%                   in [ms]
%       fs:         sampling frequency (default: 1KHz) [Hz]
%       fid_vec:    if some subsegments should not be used for finding the
%                   optimal threshold of the P&Tthen input the indices of
%                   the corresponding points here
%       SIGN_FORCE: force sign of peaks (positive value/negative value).
%                   Particularly usefull if we do window by window detection and want to
%                   unsure the sign of the peaks to be the same accross
%                   windows (which is necessary to build an FECG template)
%       debug:      1: plot to bebug, 0: do not plot
%
% outputs
%   qrs_pos:        indexes of detected peaks (in samples)
%   sign:           sign of the peaks (a pos or neg number)
%   en_thres:       energy threshold used
%
%
%
% Physionet Challenge 2014, version 1.0
% Released under the GNU General Public License
%
% Copyright (C) 2014  Joachim Behar
% Oxford university, Intelligent Patient Monitoring Group
% joachim.behar@eng.ox.ac.uk
%
% Last updated : 13-09-2014
% - bug on refrac period fixed
% - sombrero hat for prefiltering added
% - code a bit more tidy
% - condition added on flatline detection for overall segment (if flatline 
% then returns empty matrices rather than some random stuff)
%
% This program 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 2 of the License, or (at your
% option) any later version.
% This program 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.

% == managing inputs
WIN_SAMP_SZ = 7;
REF_PERIOD = 0.250; 
THRES = 0.6; 
fs = 1000; 
fid_vec = [];
SIGN_FORCE = [];
debug = 0;

switch nargin
    case 1
        % do nothing
    case 2
        REF_PERIOD=varargin{1};
    case 3
        REF_PERIOD=varargin{1}; 
        THRES=varargin{2};
    case 4
        REF_PERIOD=varargin{1}; 
        THRES=varargin{2};
        fs=varargin{3};  
    case 5
        REF_PERIOD=varargin{1}; 
        THRES=varargin{2}; 
        fs=varargin{3}; 
        fid_vec=varargin{4};
    case 6
        REF_PERIOD=varargin{1}; 
        THRES=varargin{2}; 
        fs=varargin{3};
        fid_vec=varargin{4}; 
        SIGN_FORCE=varargin{5};
    case 7
        REF_PERIOD=varargin{1}; 
        THRES=varargin{2}; 
        fs=varargin{3};
        fid_vec=varargin{4};
        SIGN_FORCE=varargin{5};          
        debug=varargin{6};
    case 8
        REF_PERIOD=varargin{1}; 
        THRES=varargin{2}; 
        fs=varargin{3};
        fid_vec=varargin{4};
        SIGN_FORCE=varargin{5};          
        debug=varargin{6};
        WIN_SAMP_SZ = varargin{7};
    otherwise
        error('qrs_detect: wrong number of input arguments \n');
end


[a b] = size(ecg);
if(a>b); NB_SAMP=a; elseif(b>a); NB_SAMP=b; ecg=ecg'; end;
tm = 1/fs:1/fs:ceil(NB_SAMP/fs);

% == constants
MED_SMOOTH_NB_COEFF = round(fs/100);
INT_NB_COEFF = round(WIN_SAMP_SZ*fs/256); % length is 30 for fs=256Hz  
SEARCH_BACK = 1; % perform search back (FIXME: should be in function param)
MAX_FORCE = []; % if you want to force the energy threshold value (FIXME: should be in function param)
MIN_AMP = 0.1; % if the median of the filtered ECG is inferior to MINAMP then it is likely to be a flatline
               % note the importance of the units here for the ECG (mV) 
NB_SAMP = length(ecg); % number of input samples

try
    % == Bandpass filtering for ECG signal
    % this sombrero hat has shown to give slightly better results than a
    % standard band-pass filter. Plot the frequency response to convince
    % yourself of what it does
    b1 = [-7.757327341237223e-05  -2.357742589814283e-04 -6.689305101192819e-04 -0.001770119249103 ...
         -0.004364327211358 -0.010013251577232 -0.021344241245400 -0.042182820580118 -0.077080889653194...
         -0.129740392318591 -0.200064921294891 -0.280328573340852 -0.352139052257134 -0.386867664739069 ...
         -0.351974030208595 -0.223363323458050 0 0.286427448595213 0.574058766243311 ...
         0.788100265785590 0.867325070584078 0.788100265785590 0.574058766243311 0.286427448595213 0 ...
         -0.223363323458050 -0.351974030208595 -0.386867664739069 -0.352139052257134...
         -0.280328573340852 -0.200064921294891 -0.129740392318591 -0.077080889653194 -0.042182820580118 ...
         -0.021344241245400 -0.010013251577232 -0.004364327211358 -0.001770119249103 -6.689305101192819e-04...
         -2.357742589814283e-04 -7.757327341237223e-05];

    b1 = resample(b1,fs,250);
    bpfecg = filtfilt(b1,1,ecg)';
    
    if (sum(abs(ecg-median(ecg))>MIN_AMP)/NB_SAMP)>0.05
        % if 20% of the samples have an absolute amplitude which is higher
        % than MIN_AMP then we are good to go.
        
        % == P&T operations
        dffecg = diff(bpfecg');  % (4) differentiate (one datum shorter)
        sqrecg = dffecg.*dffecg; % (5) square ecg
        intecg = filter(ones(1,INT_NB_COEFF),1,sqrecg); % (6) integrate
        mdfint = medfilt1(intecg,MED_SMOOTH_NB_COEFF);  % (7) smooth
        delay  = ceil(INT_NB_COEFF/2); 
        mdfint = circshift(mdfint,-delay); % remove filter delay for scanning back through ECG

        % look for some measure of signal quality with signal fid_vec? (FIXME)
        if isempty(fid_vec); mdfintFidel = mdfint; else mdfintFidel(fid_vec>2) = 0; end;

        % == P&T threshold
        if NB_SAMP/fs>90; xs=sort(mdfintFidel(fs:fs*90)); else xs = sort(mdfintFidel(fs:end)); end;

        if isempty(MAX_FORCE)
           if NB_SAMP/fs>10
                ind_xs = ceil(98/100*length(xs)); 
                en_thres = xs(ind_xs); % if more than ten seconds of ecg then 98% CI
            else
                ind_xs = ceil(99/100*length(xs)); 
                en_thres = xs(ind_xs); % else 99% CI  
            end 
        else
           en_thres = MAX_FORCE;
        end

        % build an array of segments to look into
        poss_reg = mdfint>(THRES*en_thres); 

        % in case empty because force threshold and crap in the signal
        if isempty(poss_reg); poss_reg(10) = 1; end;

        % == P&T QRS detection & search back
        if SEARCH_BACK
            indAboveThreshold = find(poss_reg); % ind of samples above threshold
            RRv = diff(tm(indAboveThreshold));  % compute RRv
            medRRv = median(RRv(RRv>0.01));
            indMissedBeat = find(RRv>1.5*medRRv); % missed a peak?
            % find interval onto which a beat might have been missed
            indStart = indAboveThreshold(indMissedBeat);
            indEnd = indAboveThreshold(indMissedBeat+1);

            for i=1:length(indStart)
                % look for a peak on this interval by lowering the energy threshold
                poss_reg(indStart(i):indEnd(i)) = mdfint(indStart(i):indEnd(i))>(0.5*THRES*en_thres);
            end
        end

        % find indices into boudaries of each segment
        left  = find(diff([0 poss_reg'])==1);  % remember to zero pad at start
        right = find(diff([poss_reg' 0])==-1); % remember to zero pad at end

        % looking for max/min?
        if SIGN_FORCE
            sign = SIGN_FORCE;
        else
            nb_s = length(left<30*fs);
            loc  = zeros(1,nb_s);
            for j=1:nb_s
                [~,loc(j)] = max(abs(bpfecg(left(j):right(j))));
                loc(j) = loc(j)-1+left(j);
            end
            sign = mean(ecg(loc));  % FIXME: change to median?  
        end

        % loop through all possibilities 
        compt=1;
        NB_PEAKS = length(left);
        maxval = zeros(1,NB_PEAKS);
        maxloc = zeros(1,NB_PEAKS);
        for i=1:NB_PEAKS
            if sign>0
                % if sign is positive then look for positive peaks
                [maxval(compt) maxloc(compt)] = max(ecg(left(i):right(i)));
            else
                % if sign is negative then look for negative peaks
                [maxval(compt) maxloc(compt)] = min(ecg(left(i):right(i)));
            end
            maxloc(compt) = maxloc(compt)-1+left(i); % add offset of present location

            % refractory period - has proved to improve results
            if compt>1
                if maxloc(compt)-maxloc(compt-1)<fs*REF_PERIOD && abs(maxval(compt))<abs(maxval(compt-1))
                    maxloc(compt)=[]; maxval(compt)=[];
                elseif maxloc(compt)-maxloc(compt-1)<fs*REF_PERIOD && abs(maxval(compt))>=abs(maxval(compt-1))
                    maxloc(compt-1)=[]; maxval(compt-1)=[];
                else
                    compt=compt+1;
                end
            else
                % if first peak then increment
                compt=compt+1;
            end
        end

        qrs_pos = maxloc; % datapoints QRS positions 
        R_t = tm(maxloc); % timestamps QRS positions
        R_amp = maxval; % amplitude at QRS positions
        hrv = 60./diff(R_t); % heart rate
    else
        % this is a flat line
        qrs_pos = [];
        R_t = [];
        R_amp = [];
        hrv = [];
        sign = [];
        en_thres = [];
    end
catch ME
    rethrow(ME);
    for enb=1:length(ME.stack); disp(ME.stack(enb)); end;
    qrs_pos = [1 10 20]; sign = 1; en_thres = 0.5; 
end

% == plots
if debug
    figure;
    FONTSIZE = 20;
    ax(1) = subplot(4,1,1); plot(tm,ecg); hold on;plot(tm,bpfecg,'r')
        title('raw ECG (blue) and zero-pahse FIR filtered ECG (red)'); ylabel('ECG');
        xlim([0 tm(end)]);  hold off;
    ax(2) = subplot(4,1,2); plot(tm(1:length(mdfint)),mdfint);hold on;
        plot(tm,max(mdfint)*bpfecg/(2*max(bpfecg)),'r',tm(left),mdfint(left),'og',tm(right),mdfint(right),'om'); 
        title('Integrated ecg with scan boundaries over scaled ECG');
        ylabel('Int ECG'); xlim([0 tm(end)]); hold off;
    ax(3) = subplot(4,1,3); plot(tm,bpfecg,'r');hold on;
        plot(R_t,R_amp,'+k');
        title('ECG with R-peaks (black) and S-points (green) over ECG')
        ylabel('ECG+R+S'); xlim([0 tm(end)]); hold off;
    ax(4) = subplot(4,1,4); plot(R_t(1:length(hrv)),hrv,'r+')
        hold on, title('HR')
        ylabel('RR (s)'); xlim([0 tm(end)]);
    
    %linkaxes(ax,'x');
    set(gca,'FontSize',FONTSIZE);
    allAxesInFigure = findall(gcf,'type','axes');
    set(allAxesInFigure,'fontSize',FONTSIZE);
end


% NOTES
%   Finding the P&T energy threshold: in order to avoid crash due to local 
%   huge bumps, threshold is choosen at 98-99% of amplitude distribution. 
%   first sec removed for choosing the thres because of filter init lag.
%   
%   Search back: look for missed peaks by lowering the threshold in area where the 
%   RR interval variability (RRv) is higher than 1.5*medianRRv
% 
%   Sign of the QRS (signForce): look for the mean sign of the R-peak over the
%   first 30sec when looking for max of abs value. Then look for the
%   R-peaks over the whole record that have this given sign. This allows to
%   not alternate between positive and negative detections which might
%   happen in some occasion depending on the ECG morphology. It is also
%   better than forcing to look for a max or min systematically.