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   -> Volume 11, Issue 9

Answer: DWT for matrices with arbitrary size (non-dyadic or non-square)
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Li Yiwei (

PostPosted: Tue Oct 21, 2003 1:21 am    
Subject: Answer: DWT for matrices with arbitrary size (non-dyadic or non-square)
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Reply to WD 11.7 Topic 5409.


Recently, a new algorithm called BFWT has been developed for applying "almost FWT" to images or matrices with arbitrary size. In fact, if the size is dyadic, BFWT is exactly FWT.

BFWT originated from an attempt to apply fast wavelet transforms to matrices with arbitrary size which were generated by a BEM program for solving the solar force-free magnetic field equation.

Since the standard FWT cannot be applied directly to a matrix with size of non-power-of-two, we have to make modifications either to the target matrix or to the transform itself to match them together. Usually, in signal processing, the matrix with non-dyadic length is padded with zeros to a length of power of two in order to fit with FWT ( or FFT ). This is a method which makes modifications to the target matrix.

Alteratively, BFWT makes modifications to the FWT itself.

BFWT has been implemented in FORTRAN , and it has been successfully applied to fast solution of BEM system Ax=b,where A is a dense matrix with arbitrary size. In BEM application,the BFWT is used to compress the dense coefficient matrix A.

BFWT can certainly be used to compress image and other signal. It can also be looked as an orthonomal base with wavelet characteristic.

If anyone is interested in BFWT, please me a email.

Algorithm of BFWT is developed by Li Yiwei under instructions of Prof. Song Guoxiang and Prof. Yan Yihua.

Li Yiwei
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