How to keep track of where each measurement originates from?

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Goncalo Costa 2021-7-14

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回答： Prachi Kulkarni 2021-8-11

When creating a pattern/mask for single-pixel imaging of a picture, I use a different delta function for each measurement, and this is all done withing a for loop as follows:

img = double(im2gray(picture))   %grayscale of n pixel image , read here as picture
for i = 1:n^2
    delta = zeros(n,n); %delta is  nxn matrix where a single element is 1. 
    delta(i) = 1;  % This element changes with each loop.
    
    A = real(ifft2(delta))  %mask
    B(i) = sum(img.*A, 'All'); %light coming through
     
end

How do I keep track of where each measurement comes from. ie, which delta function corresponds to a measurement [1].

The code is intended to be applied to the use of PCA to the data (which I am still uncertain as how to do) to decrease the number of measurements needed to analyse an image.

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Walter Roberson 2021-7-16

You do not use A after you compute it, but you use P?

Goncalo Costa 2021-7-21

sorry that was a silly mistake when simplifying the code for the question

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Answer 1

Prachi Kulkarni 2021-8-11

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Hi,

The index variable i itself is an indicator of which delta function corresponds to which measurement.

For example, for the 10th measurement B(10), the delta function can be regenerated whenever required as-

delta = zeros(n,n);
delta(10) = 1;

Alternatively, if you want to store all the delta functions (although it may not be memory-efficient), you can rewrite your code as-

img = double(im2gray(picture));  % grayscale of n pixel image , read here as picture
delta = zeros(n,n,n^2);          % collection of all delta functions
for i = 1:n^2
    deltaSingle = zeros(n,n);    % delta is  nxn matrix where a single element is 1. 
    deltaSingle(i) = 1;          % this element changes with each loop
    delta(:,:,i) = deltaSingle;  % placing individual delta in the collection of delta functions
end
    
A = real(ifft2(delta));          % mask created for all delta functions simultaneously
B = squeeze(sum(img.*A, [1 2]))'; % light coming through computed for delta functions simultaneously
     

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