SVD_GRAY is a MATLAB program which reads a file containing a grayscale image and uses the singular value decomposition (SVD) to compute and display a series of low rank approximations to the image.
In MATLAB, images can be thought of as numeric arrays (although you do have to convert them from the uint8 numeric format used for images to the double format used for numeric arrays.)
Therefore, an MxN image A has an SVD decomposition A = U*S*V'.
For any 1 <= R <= min(M,N), a low rank approximation to A is formed by
Ar = U(1:m,1:r) * S(1:r,1:r) * V(1:n,1:r)';
Properties of the SVD guarantee that Ar is the best possible rank R
approximation to the data in A. This means it is often possible to get
a good approximation to A using much less data.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
SVD_GRAY is available in a MATLAB version.
SVD_BASIS, a MATLAB program which applies the singular value decomposition (SVD) to a collection of data vectors, extracting dominant modes;
svd_test, a MATLAB program which demonstrates the singular value decomposition (SVD) for a simple example.
SVD_FINGERPRINT, a MATLAB program which reads a file containing a fingerprint image and uses the Singular Value Decomposition (SVD) to compute and display a series of low rank approximations to the image.
SVD_SNOWFALL, a MATLAB program which reads a file containing historical snowfall data and analyzes the data with the Singular Value Decomposition (SVD).
SVD_TRUNCATED, a MATLAB program which demonstrates the computation of the reduced or truncated Singular Value Decomposition (SVD) that is useful for cases when one dimension of the matrix is much smaller than the other.