Hadamard Transform
Hi
WHT : Walsh Hadamard Transform
I have uploaded basis images of WHT for case N=4;
we have 16 ,4x4 basis Hadamard images.
our original 4x4 image is projected on basis images & corresponding WHT coefficient are obtained.
Properties of WHT:
1)WHT is a vary fast transform i.e. O(N)
2)WHT is a popular Digital transform since its kernel function is only consisted from 0 and 1(black & white)
3)WHT is a Unitary transform i.e.
transpose(H)=H^-1
4)being unitary it has to be a Orthonormal transform
i.e. its basis vectors build a Basis in space.
5)WHT is a transform with good to very good energy compaction i.e the result of applying WHT to a set of data will have a near-diagonal covariance matrix with lots of zero!!
and finally I agrre with our friend Pmonon .
juice of classical transformation theory is to represent data in another space so that data in new space our less correlated.
for detailed discussion refer to:
1)Fundamentals of digital image processing Anil.Jain
2)Digital Image Processing Gonzalez & Woods
hope it helped
Armin