Question

this post is related to my previous question : image processing in matlab
as I have uploaded my algorithme there.
the think is that I am trying to change the filtering part of the code.
in matlab filter.m function can accpet filter(B, A, my pixels evolutions in Time) and it return me the filtered values.
but at the moment I have to pass the the whole time series together.

but the problem is that now I want to change the code in a way instead of passing the whole timeseries into the filter, I want to pass one value at a time, but I want filter function treat the value like the nth value not the first valu.
I have created a sudo code, as I am injecting one picture into the code, but I dont know how can change the filtering part., any body has any idea??

clear all
j=1;
for i=0:3000
  str = num2str(i);
  str1 = strcat(str,'.mat');
  load(str1);
  D{j}=A(20:200,130:230);
  j=j+1;
end
N=5;
w = [0.00000002 0.05;0.05 0.1;0.1 0.15;0.15 0.20;
     0.20 0.25;0.25 0.30;0.30 0.35;0.35 0.40;
     0.40 0.45;0.45 0.50;0.50 0.55;0.55 0.60;
     0.60 0.65;0.65 0.70;0.70 0.75;0.75 0.80;
     0.80 0.85;0.85 0.90;0.90 0.95;0.95 0.99999999];
for ind=1:20
  wn = w(ind,:);
  [b,a] = butter(N,wn);
  bCoeff(ind,:)=b;
  aCoeff(ind,:)=a;
end

ts=[];
sumLastImages=[];
for k=1:10 %number of images
  for bands=1:20 %number of bands
    for i=1:10 %image h
      for j=1:10 %image w
        pixelValue = D{k}(i,j);          
        % reflectivity elimination        
        % for the current pixel, have the summation of the same position from before 
        % images and create a mean value base on the temporal values
        sumLastImages(i,j)=pixelValue+sumLastImages(i,j);
        meanValue = sumLastImages(i,j)/k;

        if(meanValue==0)            
          filteredimages{bands}(i,j)=0; 
          continue;
        else
          pixel_calculated_meanvalue = pixelValue/meanValue; 
        end                      
        % filter part that need to be changed, and because we are adding 
        % one value then the reutrn of the filter is one too         
        ts_f = filter(bCoeff(bands,:), aCoeff(bands,:), ...
                      pixel_calculated_meanvalue);                         
        filteredimages{bands}(i,j)=ts_f;            
      end     
    end       

    finalImagesSummation{bands}(:,:) = ...
      (filteredimages{bands}(:,:)^2)+finalImagesSummation{bands}(:,:);
    finalImages{bands}(:,:)=finalImagesSummation/k;
  end
end

EDIT
I managed to change the code like this, which now I load the fist 200 images, and after that I am able to inject the images one by one into the filter, but now the problem is that I am getting "Out of memory. Type HELP MEMORY for your options." error for big
images.
here is my code any idea to efficent the code :

%%
cd('D:\MatlabTest\06-06-Lentils');
clear all

%%

N=5;
W = [0.0 0.10;0.10 0.20;0.20 0.30;0.30 0.40;
     0.40 0.50;0.50 0.60 ;0.60 0.70;0.70 0.80 ;
     0.80 0.90;0.90 1.0];

[bCoeff{1},aCoeff{1}] = butter(N,0.1,'Low');
for ind=2:9
  wn = W(ind,:);
  [b,a] = butter(N,wn);
  bCoeff{ind}=b;
  aCoeff{ind}=a;
end
[bCoeff{10},aCoeff{10}] = butter(N,0.9,'high');

%%
j=1;

D = zeros(200,380,320);

T = 200;
K = 0:399;
l = T+1;
Yout = cell(1,10);
figure;

for i = 1:length(K)-200
  disp(i)

  if i == 1
    for j = 1:T
      str = int2str(K(1)+j-1);
      str1 = strcat(str,'.mat');
      load(str1);
      D(j,1:380,1:320) = A;
    end

  else

    str = int2str(l);
    str1 = strcat(str,'.mat');
    load(str1);

    temp = D(2:200,1:380,1:320) ;
    temp(200,1:380,1:320) = A;
    D = temp;
    clear temp
    l = l +1;

  end


  for p = 1:380
    for q = 1:320
      x = D(:,p,q) - mean(D(:,p,q));

      for k = 1:10
        temp = filter(bCoeff{k},aCoeff{k},x);
        if i == 1
          Yout{k}(p,q) = mean(temp);
        else
          Yout{k}(p,q) = (Yout{k}(p,q)  + mean(temp))/2;
        end
      end
    end
  end

  for k = 1:10
    subplot(5,2,k)
    subimage(Yout{k}*1000,[0 255]);
    color bar
    colormap jet
  end
  pause(0.01);
end

disp('Done Loading...')

Answer 1

No need to rewrite the filter function, there is a simple solution!

If you want to feed filter with one sample at a time, you need to pass the state parameters as well so that each input sample is processed depending on its predecessor. After filtering, the new state is actually returned as a second parameter, so that most of the work is already done by MATLAB for you. This is good news!

For the sake of readability, allow me to temporarily replace your variable names with simple letters:

a = aCoeff(bands, :);    
b = bCoeff(bands, :);
x = pixel_calculated_meanvalue;

ts_f is represented by y.

And so, this:

y = filter(b, a, x);

is actually equivalent to this:

N = numel(x);
y = zeros(N, 1);                             %# Preallocate memory for output
z = zeros(max(length(a), length(b)) - 1, 1); %# This is the initial filter state
for i = 1:N
    [y(i), z] = filter(b, a, x(i), z);
end

You can check for yourself that the result is the same!

For your example, the code would be:

N = numel(pixel_calculated_meanvalue);
ts_f = zeros(N, 1);
z = zeros(max(length(aCoeff(bands, :)), length(bCoeff(bands, :))) - 1, 1); 
for i = 1:N
    [ts_f(i), z] = filter(bCoeff(bands, :), aCoeff(bands, :), ...
        pixel_calculated_meanvalue(i), z);
end

With this method you can process one input sample at a time, just make sure you store the last filter state after every filter call. If you plan on using multiple filters, you’ll have to store a state vector per filter!