Ecg信号QRS波峰检测：A Real-Time QRS Detection Algorithm (Pan-Tompkins法)

Pan-Tompkins法是R峰检测的经典方法，被引量高达6000+次。

Pan J, Tompkins W J. A real-time QRS detection algorithm[J]. IEEE transactions on biomedical engineering, 1985 (3): 230-236.

本文对论文流程进行了总结，并参考BioSigKit项目，复现了论文代码。

流程图：

代码如下：

• 第一部分是信号读入，这里使用MIT_BIH信号的100，读入10000个数据点
• 第二部分是R峰检测

clc; clear;

%% 读入数据
%------ SPECIFY DATA ------------------------------------------------------
%------ 指定数据文件 -------------------------------------------------------
PATH= 'E:\MATLAB\bin\ShuoShi\MIT'; % 指定数据的储存路径
HEADERFILE= '100.hea';      % .hea 格式，头文件，可用记事本打开
ATRFILE= '100.atr';         % .atr 格式，属性文件，数据格式为二进制数
DATAFILE='100.dat';         % .dat 格式，ECG 数据
SAMPLES2READ=10000;          % 指定需要读入的样本数
                            % 若.dat文件中存储有两个通道的信号:
                            % 则读入 2*SAMPLES2READ 个数据 


fprintf(1,'\\n$> WORKING ON %s ...\n', HEADERFILE); % 在Matlab命令行窗口提示当前工作状态
% 
% 【注】函数 fprintf 的功能将格式化的数据写入到指定文件中。
% 表达式：count = fprintf(fid,format,A,...)
% 在字符串'format'的控制下，将矩阵A的实数数据进行格式化，并写入到文件对象fid中。该函数返回所写入数据的字节数 count。
% fid 是通过函数 fopen 获得的整型文件标识符。fid=1，表示标准输出（即输出到屏幕显示）；fid=2，表示标准偏差。
%
signalh= fullfile(PATH, HEADERFILE);    % 通过函数 fullfile 获得头文件的完整路径
fid1=fopen(signalh,'r');    % 打开头文件，其标识符为 fid1 ，属性为'r'--“只读”
z= fgetl(fid1);             % 读取头文件的第一行数据，字符串格式
A= sscanf(z, '%*s %d %d %d',[1,3]); % 按照格式 '%*s %d %d %d' 转换数据并存入矩阵 A 中
nosig= A(1);    % 信号通道数目
sfreq=A(2);     % 数据采样频率
clear A;        % 清空矩阵 A ，准备获取下一行数据
for k=1:nosig           % 读取每个通道信号的数据信息
    z= fgetl(fid1);
    A= sscanf(z, '%*s %d %d %d %d %d',[1,5]);
    dformat(k)= A(1);           % 信号格式; 这里只允许为 212 格式
    gain(k)= A(2);              % 每 mV 包含的整数个数
    bitres(k)= A(3);            % 采样精度（位分辨率）
    zerovalue(k)= A(4);         % ECG 信号零点相应的整数值
    firstvalue(k)= A(5);        % 信号的第一个整数值 (用于偏差测试)
end;
fclose(fid1);
clear A;

%------ LOAD BINARY DATA --------------------------------------------------
%------ 读取 ECG 信号二值数据 ----------------------------------------------
%
if dformat~= [212,212], error('this script does not apply binary formats different to 212.'); end;
signald= fullfile(PATH, DATAFILE);            % 读入 212 格式的 ECG 信号数据
fid2=fopen(signald,'r');
A= fread(fid2, [3, SAMPLES2READ], 'uint8')';  % matrix with 3 rows, each 8 bits long, = 2*12bit
fclose(fid2);
% 通过一系列的移位（bitshift）、位与（bitand）运算，将信号由二值数据转换为十进制数
M2H= bitshift(A(:,2), -4);        %字节向右移四位，即取字节的高四位
M1H= bitand(A(:,2), 15);          %取字节的低四位
PRL=bitshift(bitand(A(:,2),8),9);     % sign-bit   取出字节低四位中最高位，向右移九位
PRR=bitshift(bitand(A(:,2),128),5);   % sign-bit   取出字节高四位中最高位，向右移五位
M( : , 1)= bitshift(M1H,8)+ A(:,1)-PRL;
M( : , 2)= bitshift(M2H,8)+ A(:,3)-PRR;
if M(1,:) ~= firstvalue, error('inconsistency in the first bit values'); end;
switch nosig
case 2
    M( : , 1)= (M( : , 1)- zerovalue(1))/gain(1);
    M( : , 2)= (M( : , 2)- zerovalue(2))/gain(2);
    TIME=(0:(SAMPLES2READ-1))/sfreq;
case 1
    M( : , 1)= (M( : , 1)- zerovalue(1));
    M( : , 2)= (M( : , 2)- zerovalue(1));
    M=M';
    M(1)=[];
    sM=size(M);
    sM=sM(2)+1;
    M(sM)=0;
    M=M';
    M=M/gain(1);
    TIME=(0:2*(SAMPLES2READ)-1)/sfreq;
otherwise  % this case did not appear up to now!
    % here M has to be sorted!!!
    disp('Sorting algorithm for more than 2 signals not programmed yet!');
end;
clear A M1H M2H PRR PRL;
fprintf(1,'\\n$> LOADING DATA FINISHED \n');

%------ LOAD ATTRIBUTES DATA ----------------------------------------------
atrd= fullfile(PATH, ATRFILE);      % attribute file with annotation data
fid3=fopen(atrd,'r');
A= fread(fid3, [2, inf], 'uint8')';
fclose(fid3);
ATRTIME=[];
ANNOT=[];
sa=size(A);
saa=sa(1);
i=1;
while i<=saa
    annoth=bitshift(A(i,2),-2);
    if annoth==59
        ANNOT=[ANNOT;bitshift(A(i+3,2),-2)];
        ATRTIME=[ATRTIME;A(i+2,1)+bitshift(A(i+2,2),8)+...
                bitshift(A(i+1,1),16)+bitshift(A(i+1,2),24)];
        i=i+3;
    elseif annoth==60
        % nothing to do!
    elseif annoth==61
        % nothing to do!
    elseif annoth==62
        % nothing to do!
    elseif annoth==63
        hilfe=bitshift(bitand(A(i,2),3),8)+A(i,1);
        hilfe=hilfe+mod(hilfe,2);
        i=i+hilfe/2;
    else
        ATRTIME=[ATRTIME;bitshift(bitand(A(i,2),3),8)+A(i,1)];
        ANNOT=[ANNOT;bitshift(A(i,2),-2)];
   end;
   i=i+1;
end;
ANNOT(length(ANNOT))=[];       % last line = EOF (=0)
ATRTIME(length(ATRTIME))=[];   % last line = EOF
clear A;
ATRTIME= (cumsum(ATRTIME))/sfreq;
ind= find(ATRTIME <= TIME(end));
ATRTIMED= ATRTIME(ind);
ANNOT=round(ANNOT);
ANNOTD= ANNOT(ind);

%------ DISPLAY DATA ------------------------------------------------------
figure(1); clf, box on, hold on
plot(TIME, M(:,1),'r');


% if nosig==2
%     plot(TIME, M(:,2),'b');
% end;
% for k=1:length(ATRTIMED)
%     text(ATRTIMED(k),0,num2str(ANNOTD(k)));
% end;


xlim([TIME(1), TIME(end)]);
xlabel('Time / s'); ylabel('Voltage / mV');
string=['ECG signal ',DATAFILE];
title(string);
fprintf(1,'\\n$> DISPLAYING DATA FINISHED \n');

% -------------------------------------------------------------------------
fprintf(1,'\\n$> ALL FINISHED \n');



%% QRS检测
ecg = M(:,1)';


if ~isvector(ecg)
  error('ecg must be a row or column vector');
end
ecg = ecg(:); % vectorize


Fs = 200;
flag = 1;
%ecg是输入的信号，Fs是抽样频率，plot是是否绘图，绘图为1，不绘图为0


% 经过滤波求导平方均值后的信号和阈值
Signal_mean = [];
Signal_mean_index = [];
Thresh_Signal_mean = 0;
Thresh_Noise_mean = 0;

% 经过滤波求导平方均值后的噪声
Noise_mean = [];
Noise_mean_index = [];

% 经过带通滤波后的信号和阈值
Signal_filter = [];
Signal_filter_index = [];
Thresh_Signal_filter = 0;
Thresh_Noise_filter = 0;

% 当前信号、当前噪声大小
Signal_temp_mean = 0;
Noise_temp_mean = 0;
Signal_temp_filter = 0;
Noise_temp_filter = 0;

% 经过滤波求导平方均值后的信号和噪声的暂存
Signal_mean_buf = [];
Noise_mean_buf = [];


% 经过带通滤波后的信号和噪声的暂存
Signal_filter_buf = [];
Noise_filter_buf = [];

Thresh_Signal_mean_buf = [];
Thresh_Signal_filter_buf = [];

% 8次有规律的心率间隔
regular_RR_interval = 0;
% 8次心率间隔
mean_interval = 0;
% 心率间隔，regular_RR_interval有值就是regular_RR_interval，不然就是mean_interval
RR_interval =  0;

%<0.36Fs时判断是否是T波，如果确实是R波就是0，否则为1
R_Flag = 0;

%% 滤波1，先低通后高通
if Fs == 200
    
    %低通，H(z) = ((1 - z^(-6))^2)/(1 - z^(-1))^2
    
    b = [1 0 0 0 0 0 -2 0 0 0 0 0 1];
    a = [1 -2 1];
    
    h_l = filter(b,a, [1,zeros(1,12)]);
    
    ecg_l = conv(ecg, h_l);
    ecg_l = ecg_l / max(abs(ecg_l));
    
    
    %高通 H(z) = (-1+32z^(-16)+z^(-32))/(1+z^(-1))
    
    b = [-1 zeros(1,15) 32 -32 zeros(1,14) 1];
    a = [1 -1];
    
    h_h = filter(b,a, [1, zeros(1,32)]);
    ecg_filter = conv(ecg_l, h_h);
    ecg_filter = ecg_filter / max(abs(ecg_filter));

%% 滤波2，直接buttord滤波，5-15Hz的数字带通滤波器
else
    wp = [5 15] * 2 / Fs;
    
    [B,A] = butter(3, wp);%3阶滤波器
    
    ecg_filter = filtfilt(B,A, ecg);
    ecg_filter = ecg_filter / max(abs(ecg_filter));
    
end

%% 求导 H(z) = (1/8T)(-z^(-2) - 2z^(-1) + 2z + z^(2))
    
    h_d = [-1 -2 0 2 1];
    ecg_deri = conv(h_d, ecg_filter);
    ecg_deri = ecg_deri / max(abs(ecg_deri));

%% 平方
    
    ecg_square = ecg_deri .^ 2;
    
%% 窗口均值化
    Window_width = 0.15 * Fs;
    
    ecg_mean = conv(ecg_square, ones(1, Window_width) / Window_width);

%% 绘图
if flag
    figure;
    if Fs == 200
    ax(1)=subplot(321);plot(ecg);axis tight;title('Raw ECG Signal');
    ax(2)=subplot(322);plot(ecg_l);axis tight;title('After LowerPass');
    else
        ax(1)=subplot(3,2,[1,2]);plot(ecg);axis tight;title('Raw ECG Signal');
    end
    
    ax(3) = subplot(323);plot(ecg_filter);axis tight;title('After band filter');
    ax(4) = subplot(324);plot(ecg_deri);axis tight;title('After Derivative');
    ax(5) = subplot(325);plot(ecg_square);axis tight;title('After Square');
    ax(6) = subplot(326);plot(ecg_mean);axis tight;title('After Mean');
    
end


%% 通过findpeaks找到局部的波峰

[peaks, locs] = findpeaks(ecg_mean, 'MINPEAKDISTANCE', round(0.2 * Fs));


%% 对阈值进行初始化，使用前2s的数据


% 初始化信号阈值和噪声阈值，只使用平方并均值后信号前两秒
%信号阈值为前两秒最大值的0.33,噪声阈值为前两秒平均值的0.5
Thresh_Signal_mean = max(ecg_mean(1:2*Fs)) / 3;
Thresh_Noise_mean = mean(ecg_mean(1:2*Fs)) / 2;

Signal_temp_mean = Thresh_Signal_mean;
Noise_temp_mean = Thresh_Noise_mean;

% 初始化信号阈值和噪声阈值，只使用带通滤波后信号前两秒
%信号阈值为前两秒最大值的0.33,噪声阈值为前两秒平均值的0.5
Thresh_Signal_filter = max(ecg_filter(1:2*Fs)) / 3;
Thresh_Noise_filter = mean(ecg_filter(1:2*Fs)) / 2;

Signal_temp_filter = Thresh_Signal_filter;
Noise_temp_filter = Thresh_Noise_filter;


%% 对每个波峰进行处理
for i = 1 : length(peaks)  
    
    %% 找到滤波后信号波峰的位置，index是相对值
    if locs(i) - round(0.15 * Fs) >= 1 && locs(i) <= length(ecg_filter)
        [peak_filter, index_filter] = max( ecg_filter(locs(i) - round(0.15 * Fs) : locs(i)));
        index_filter = locs(i) - round(0.15 * Fs) + index_filter - 1;
    else
        if i == 1 % i = 1是时候index是绝对值
            [peak_filter, index_filter] = max( ecg_filter(1 : locs(i)));
        else %index是相对值
            [peak_filter, index_filter] = max( ecg_filter(locs(i) - round(0.15 * Fs) : end));
            index_filter = locs(i) - round(0.15 * Fs) + index_filter - 1 ;
        end
    end
    %% 判断间隔，如果大于1.66要先处理被遗漏的R波，这样才能保持顺序
    
    %要有9个R波，才有8个间隔，才能判断是否大于1.66
    if length(Signal_mean) >= 9
        RR_diff = diff(Signal_mean_index(end - 8:end));
        mean_interval = mean(RR_diff);
        
        temp_interval = Signal_mean_index(end) - Signal_mean_index(end - 1);
        
        if(temp_interval >= 0.92 * mean_interval || temp_interval <= 1.16 * mean_interval)
            Thresh_Signal_mean = Thresh_Signal_mean / 2;
            Thresh_Signal_filter = Thresh_Signal_filter / 2;
        else
            regular_RR_interval = mean_interval;
        end
    end
    
    if regular_RR_interval
        RR_interval = regular_RR_interval;
    elseif mean_interval
        RR_interval = mean_interval;
    else
        RR_interval = 0;
    end
    
    % 心率间隔有值的话
    if RR_interval
        % 超过了1.66 RR，说明中间有漏检,不应期为0.2ms
        if locs(i) - Signal_mean_index(end) >= 1.66 * RR_interval
            [pk_temp, pk_temp_ind] = max( ecg_mean(Signal_mean_index(end) + round(0.2 * Fs) : locs(i) - round(0.2 * Fs)));
            
            pk_temp_ind = Signal_mean_index(end) + round(0.2 * Fs) + pk_temp_ind - 1;
            
            % 均值信号大于噪声峰值，加到buf里
            if pk_temp >= Thresh_Noise_mean
                Signal_mean = [Signal_mean pk_temp];
                Signal_mean_index = [Signal_mean_index pk_temp_ind];
                
                %找到滤波信号的位置
                if pk_temp_ind <= length(ecg_filter)
                    [pk_filter_temp, pk_filter_temp_ind] = max(ecg_filter(pk_temp_ind - round(0.15 * Fs) :  pk_temp_ind));
                else
                    [pk_filter_temp, pk_filter_temp_ind] = max(ecg_filter(pk_temp_ind - round(0.15 * Fs) :  length(ecg_filter)));
                end
                
                pk_filter_temp_ind = ecg_filter(pk_temp_ind - round(0.15 * Fs) + pk_filter_temp_ind - 1);
                
                % 滤波信号也大于噪声阈值，加到buf里，同时sig使用新的更新策略
                if pk_filter_temp >= Thresh_Noise_filter
                    Signal_filter = [Signal_filter pk_filter_temp];
                    Signal_filter_index = [Signal_filter_index pk_filter_temp_ind];
                    
                    Signal_temp_filter = 0.25 * pk_filter_temp + 0.75 * Signal_temp_filter;
                end
                    
                Signal_temp_mean = 0.25 * pk_temp + 0.75 * Signal_temp_mean;

            end
        end
    end
    
    %% 当前波峰大于信号阈值
    if peaks(i) >= Thresh_Signal_mean
        
        %要有三个波才能有两个间隔
        if(length(Signal_mean) >= 3)
            
            %如果间隔小于0.36Fs,判断是T波还是噪声
            if locs(i) - Signal_mean_index(end) < round(0.36 * Fs)
                Slope_1 = mean(diff(ecg_mean(locs(i) - round(0.075 * Fs) : locs(i))));
                Slope_2 = mean(diff(ecg_mean(Signal_mean_index(end) - round(0.075 * Fs) : Signal_mean_index(end))));
                
                %斜率太小了，当前波峰识别为噪声
                if Slope_1 <= Slope_2 / 2
                    
                    Noise_mean = [Noise_mean peaks(i)];
                    Noise_mean_index = [Noise_mean_index locs(i)];
                    Noise_temp_mean = 0.25 * peaks(i) + 0.75 * Noise_temp_mean;
                    Noise_temp_filter = 0.25 * peak_filter + 0.75 * Noise_temp_filter;
                    R_Flag = 1;%是T波
                
                else%斜率够大，确实是R波
                    R_Flag = 0;%确实是T波
                end
            end
        end
        
        if R_Flag == 0

            Signal_mean = [Signal_mean peaks(i)];
            Signal_mean_index = [Signal_mean_index locs(i)];
            Signal_temp_mean = 0.125 * peaks(i) + 0.875 * Signal_temp_mean;

            if peak_filter >= Thresh_Signal_filter

                Signal_filter = [Signal_filter peak_filter];
                Signal_filter_index = [Signal_filter_index index_filter];
                Signal_temp_filter = 0.125 * peak_filter + 0.875 * Signal_temp_filter;

            end
        end
        
                    
    %% 当前波峰大于噪声阈值，但小于信号阈值,此时的波峰为噪声波峰
    elseif peaks(i) < Thresh_Signal_mean && peaks(i) >= Thresh_Noise_mean
        
        Noise_temp_mean = 0.125 * peaks(i) + 0.875 * Noise_temp_mean;
        Noise_temp_filter = 0.125 * peak_filter + 0.875 * Noise_temp_filter;
        
    %% 当前波峰小于噪声阈值,此时的波峰为噪声波峰
    else
        Noise_temp_mean = 0.125 * peaks(i) + 0.875 * Noise_temp_mean;
        Noise_temp_filter = 0.125 * peak_filter + 0.875 * Noise_temp_filter;
        
        Noise_mean = [Noise_mean peaks(i)];
        Noise_mean_index = [Noise_mean_index locs(i)];
        
    end
    
    %% 更新阈值参数
    Thresh_Signal_mean = Noise_temp_mean + 0.25 * (Signal_temp_mean - Noise_temp_mean);
    Thresh_Noise_mean = Thresh_Signal_mean / 2;
    
    Thresh_Signal_filter = Noise_temp_filter + 0.25 * (Signal_temp_filter - Noise_temp_filter);
    Thresh_Noise_filter = Thresh_Signal_filter / 2;
    
    %% 信号当前值存入buf
    Signal_mean_buf = [Signal_mean_buf Signal_temp_mean];
    Noise_mean_buf = [Noise_mean_buf Noise_temp_mean];
    

    % 经过带通滤波后的信号和噪声的暂存
    Signal_filter_buf = [Signal_filter_buf Signal_temp_filter];
    Noise_filter_buf = [Noise_filter_buf Noise_temp_filter];
    
    Thresh_Signal_mean_buf = [Thresh_Signal_mean_buf Thresh_Signal_mean];
    Thresh_Signal_filter_buf = [Thresh_Signal_filter_buf Thresh_Signal_filter];
    
    
    % 重置Flag
    R_Flag = 0;
    
end


%% 绘制结果图
if flag
    figure;
    ax(1) = subplot(211);
    plot(ecg_filter);axis tight;title('Filter Signal');
    hold on,scatter(Signal_filter_index, Signal_filter);
    hold on,plot(locs,Noise_filter_buf,'LineWidth',2,'Linestyle','--','color','k');
    hold on,plot(locs,Signal_filter_buf,'LineWidth',2,'Linestyle','-.','color','r');
    hold on,plot(locs,Thresh_Signal_filter_buf,'LineWidth',2,'Linestyle','-.','color','g');

    ax(2) = subplot(212);
    plot(ecg_mean);axis tight;title('Mean Signal');
    hold on,scatter(Signal_mean_index, Signal_mean);
    hold on,plot(locs,Noise_mean_buf,'LineWidth',2,'Linestyle','--','color','k');
    hold on,plot(locs,Signal_mean_buf,'LineWidth',2,'Linestyle','-.','color','r');
    hold on,plot(locs,Thresh_Signal_mean_buf,'LineWidth',2,'Linestyle','-.','color','g');
end

检测结果如下：