Faster 2D-Hadmard Tranform

Fast 2D-Hadamard/Walsh Transform based on Simple Matrix Vector Multiplication

Description

This function generates the 2D Walsh or Hadamard Transform of a matrix.
Where the Walsh Transform uses the sequency ordered matrix and the Hadamard the natural/hadamard ordered matrix.
The paley ordered transform is not yet implemented.

On my machine the function can transform matrices of a size up to 4096x4096 in very little time compared to the other 2D Walsh/Hadamard transform (ID 6882) which needs substantially more time.
For a 4096x4096 the transformation takes ~30s on the first call and ~20s after that (Transformation matrix is cashed)

References:
Walsh functions:
http://mathworld.wolfram.com/WalshFunction.html

Howto generate sequency ordered Hadamard Matrices:
http://ieeexplore.ieee.org/iel5/12/35157/01674860.pdf

http://dx.doi.org/
doi:10.1016/j.physletb.2003.10.071

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
Fast 2D Walsh-Hadamard Transform
This submission has inspired the following:
1D Walsh Transform, Faster 3D Walsh - Hadamard Transform (sequency, natural)

• MATLAB release: MATLAB 7.6 (R2008a)

[Jos x@y.z]

Files contains no proper help or internal comments. How do you expect others will be able to use this submission?

There are also some programming issues, e.g. log2(N) is computed multiple times.

[Andre S]

Fixed, contains now documentation and also function has now a sec. parameter to specify ordering of the basis functions.

[Jos x@y.z]

The author has indeed fixed the code issues and added a understandable help section. Well done!

btw, the classname argument is never used in the code ...

[Moe K.]

 

[Sin Yi Lee]

I have met with an error on class type when running the code. Towards the end, matlab cannot process Y = W*X*W/N...W is a double, my image X is a uint8...when i convert image X to double i got an error saying
??? Error using ==> mtimes
Input arguments must be 2-D.
Please enlighten me. Thanks.

[Sin Yi Lee]

Hey i got it..have to change image to grayscale.