How do I apply SVD (Singular Value Decomposition) to an image?

Neeta Dsouza answered . 2024-12-20 20:12:50

This sounds like it is about data types or sizes. Example

pout = imread('pout.tif');
svd(pout) % does not work
??? Undefined function or method 'svd' for input arguments of type 'uint8'.
svd(double(pout)) % works

I can however not comment on the mathematical sense of this. I you have another image format like here, you need to think about what you actually like to achieve

I = imread('board.tif');
svd(double(I))
??? Undefined function or method 'svd' for input arguments of type 'double' and
attributes 'full 3d real'.

Singular value decomposition expresses an m-by-n matrix A as A = U*S*V'. Here, S is an m-by-n diagonal matrix with singular values of A on its diagonal. The columns of the m-by-m matrix U are the left singular vectors for corresponding singular values. The columns of the n-by-n matrix V are the right singular vectors for corresponding singular values. V' is the Hermitian transpose (the complex conjugate of the transpose) of V.

To compute the singular value decomposition of a matrix, use svd. This function lets you compute singular values of a matrix separately or both singular values and singular vectors in one function call. To compute singular values only, use svd without output arguments

svd(A)

or with one output argument

S = svd(A)

To compute singular values and singular vectors of a matrix, use three output arguments:

[U,S,V] = svd(A)

svd returns two unitary matrices, U and V, the columns of which are singular vectors. It also returns a diagonal matrix, S, containing singular values on its diagonal. The elements of all three matrices are floating-point numbers. The accuracy of computations is determined by the current setting of digits.

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