How to keep track of where each measurement originates from?

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Goncalo Costa
Goncalo Costa on 14 Jul 2021
Answered: Prachi Kulkarni on 11 Aug 2021
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.

Answers (1)

Prachi Kulkarni
Prachi Kulkarni on 11 Aug 2021
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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