Two dimensional Orthogonal and Unitary transforms:

As applied to image processing, a general orthogonal series expansion for an image is a pair of transformations of the form :

		(4.1.3)

		(4.1.4)

where is called an " image transform."

It is a set of complete orthogonal discrete basis functions satisfying the properties:-

1) Orthonormality: =

2) Completeness : =

The elements v are transform coefficients and is the transformed image. The orthonomality property assures that any truncated series expansion of the form

	for ,

will minimize the sum of squares error where coefficients are given by (4.1.3). The completeness property assures that this error will be zero for .