Basis Images :

Let denote column of . Let us define the matrices and matrix inner product of two matrices and as

=

Then equ (4.1.6) and (4.1.5) give a series representation, for the images as ,

= and =

Any image can be expressed as linear combination of matrices. for k,l=0,1,2,.... N-1 are called "basis images".

Therefore any image can be expanded in a series using a complete set of basis images.

Example: Let = ; =

Transformed image = = and Basis images are found as outer product of columns of i.e

The inverse transformation = = =