[fast ICA] Matlab simulation of artifact removal based on fast ICA algorithm

1. Software version

matlab2021a

2. Theoretical knowledge of this algorithm

FAST method, the steps are as follows:

3. Core code

clc;
clear;
close all;
warning off;
addpath 'func\'
rng(3);
 
%读取数据选择
%标准信号
load edf_data.mat 
%含伪迹信号
load edf_data1.mat  
 
%%
%fast ICA算法
y01 = sensor3C;
y02 = sensor4C;

%信号归一化
data= data/max(abs(data));
y01 = sensor3C/max(abs(sensor3C));
y02 = sensor4C/max(abs(sensor4C));

figure;
subplot(211);
plot(y01);
title('观测信号1');
subplot(212);
plot(y02);
title('观测信号2');
y0 = [y01;y02];



%%
%步骤1：去掉均值
data_avg= mean(data);
y01_avg = mean(y01);
y02_avg = mean(y02); 
data    = data - data_avg;
y01     = y01-y01_avg;
y02     = y02-y02_avg;

data    = func_smooth2(data,1);
y01     = func_smooth2(y01,1);
y02     = func_smooth2(y02,1);

y1      = [y01;y02];

 

%%
%步骤2：白化
%协方差
y1_cov   = cov(y1');                    
%特征值分解
[E,D]    = eig(y1_cov);                      
%白化矩阵Q
Q        = inv(sqrt(D))*(E)';                        
%白化后信号
y1_white = Q*y1;                      
y2       = y1_white;                       

figure;
subplot(211);
plot(y2(1,:));
title('白化后信号1');
subplot(212);
plot(y2(2,:));
title('白化后信号2');


%FASTICA算法
data_fica       = y2; 
[Rnum,Cnum]     = size(data_fica);

Register_Matrix = zeros(Rnum,Rnum);      
Error2          = cell(1,Rnum);
W_sum2          = cell(1,Rnum);
Err2            = cell(1,Rnum);
for ker=1:Rnum%观测信号个数
    index        =1;
    %设置最大迭代次数
    %
    global_error = 1e-10;
    maxIteration = 500;                
    %初始值
    Wt           = randn(Rnum,1)/4;  
    Wt           = Wt/norm(Wt);  
    Err          = [];
    Error        = [];
    W_sum        = [];
    
    while index <= maxIteration | abs(abs(Wt'*Wt)-1) < global_error 
        
          W_n_1 = Wt;    
          
          Ka    = 1;
          u     = 0.4;
          
          t     = data_fica'*Wt;
          yexp  = exp(-Ka*t.^2/2);
          g     = t.*yexp;
          
          s1    =(1-Ka*t.^2);
          s2    = exp(-Ka*t.^2/2);
          dg    = s1.*s2;
          
          %加权求和判决
          if sum(abs(t'*g*Wt)) > sum(abs(data_fica*g))
             Wt_sum=(1-u)*t'*g*Wt + u*data_fica*g;  
          else
             Wt_sum=(u)*t'*g*Wt + (1-u)*data_fica*g;
          end
          
          
          tmps  =(Wt_sum)/Cnum;
          Wt    = tmps - mean(dg)*Wt;
          
          Wt    = Wt/norm(Wt);
          
          %FAST ICA计算公式
          %正交化检测
          if issparse(Register_Matrix) == 0
             Rs = abs(qr(Register_Matrix));
          else
             Rs = Register_Matrix*Register_Matrix';
          end
          Rs(1,2) = 0;
          Rs(2,1) = 0;
          
          RR      = Rs;
          
          %正交化
          Wt    = Wt - RR*Wt;                        
          Wt    = Wt/norm(Wt); 
          
          if abs(abs(Wt'*W_n_1)-1) < global_error 
             Register_Matrix(:,ker) = Wt;   
             break;
          else
             Register_Matrix(:,ker) = Register_Matrix(:,ker);  
          end
          
          if norm(Wt - W_n_1) < global_error
             Register_Matrix(:,ker) = Wt;   
             break;
          else
             Register_Matrix(:,ker) = Register_Matrix(:,ker);  
          end          
          
          index = index+1;     
          Error = [Error,abs(abs(Wt'*W_n_1)-1)];
          W_sum = [W_sum,sum(sum(Wt))];
          
          %计算ICA后的矩阵
          Y_final = Register_Matrix'*Q*y0;       
          Y_final = Y_final/max(max(abs(Y_final)));        
          
          Err     = [Err,mean(Y_final(2,:)-data)];
    end
    Err2{ker}   = Err;
    Error2{ker} = Error;
    W_sum2{ker} = W_sum;

    
end

figure;
plot(Error2{1},'b-o','linewidth',2);
xlabel('迭代次数');
ylabel('收敛误差');
grid on


%计算ICA后的矩阵
Y_final = Register_Matrix'*Q*y0;       
Register_Matrix 
Y_final = Y_final/max(max(abs(Y_final)));


%将混合矩阵重新排列并输出
figure;
subplot(311);
plot(Y_final(1,:));
title('伪迹');
subplot(312);
plot(Y_final(2,:));
title('EEG去伪迹信号');
subplot(313);
plot(data,'b');
hold on
plot(Y_final(2,:),'r');
legend('原始信号','去伪迹后信号');


N=1024;
wn = Y_final(1,:);
Pxx=10*log10(abs(fft(wn).^2)/N);
f=(0:length(Pxx)-1)/length(Pxx)*1e2;


figure;
plot(f(1:floor(length(f)/2)),Pxx(1:floor(length(f)/2)));
xlabel('频率');
ylabel('功率（dB）');
title('周期图法N=256')

D1  = Pxx(1:floor(length(f)/2));
dif1= std(D1) 


wn = Y_final(2,:);
Pxx=10*log10(abs(fft(wn).^2)/N);
f=(0:length(Pxx)-1)/length(Pxx)*1e2;


figure;
plot(f(1:floor(length(f)/2)),Pxx(1:floor(length(f)/2)));
xlabel('频率');
ylabel('功率（dB）');
title('周期图法N=256')

D2  = Pxx(1:floor(length(f)/2));
dif2= std(D2) 

4. Operation steps and simulation conclusion

 

 

5. References

[1] D  Maino,   Fa Rusi A ,  Baccigalupi C , et al. All-sky astrophysical component separation with Fast Independent Component Analysis (FastICA)[J]. Monthly Notices of the Royal Astronomical Society, 2010(1):53-68.

A28-50