matlab - How do I calculate a truncated-sum approximation? -

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screenshot of reading.

i'm take image, convert set of 3 matrices using imread(), calculate truncated-sum approximation each matrix using n=1,2,3,4,8,16,32,64,128 terms. have matrices, i'm not sure last part , reading bit vague. mean truncated-sum approximation?

update based on given answer:

i tried following:

a = double(imread("image.jpg"))/255;    [u1, s1, v1] = svd(a(:,:,1));   [u2, s2, v2] = svd(a(:,:,2));   [u3, s3, v3] = svd(a(:,:,3));  n = 128;     trunc_image = (u1(1:763,1:n)*s1(1:n,1:n)*v1(1:n,1:691))*255;  imwrite(trunc_image, "truncimg.jpg", "jpg");

...but resulting image looks this:

screenshot of resulting image

when perform svd on image i:

[u,s,v] = svd(i,'econ'); %//you matrices u, s, v

s diagonal matrix, decreasing singular values along diagonals.

approximation truncating... means can reconstruct i' zeroing out singular values in s:

i_recon = u(1:256,1:n)*s(1:n,1:n)*v(1:256,1:n).'; %//reconstruct keeping first n singular values in s.

what happens here i_recon image reconstructed n significant singular values. purpose of doing can remove less significant contributions image i, , represent i less data.

this example of reconstructed images varying n:

svd reconstruction of i


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