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# Quantization Matrix Conversion for Scaled DCT Computations

IP.com Disclosure Number: IPCOM000120107D
Original Publication Date: 1991-Mar-01
Included in the Prior Art Database: 2005-Apr-02
Document File: 2 page(s) / 70K

IBM

## Related People

Feig, E: AUTHOR [+2]

## Abstract

Disclosed is a method for converting quantization matrices derived for DCT (discrete cosine transform) compression of data to matrices for use with scaled-DCT methods (which offer significant computational savings) and a method for increasing the accuracy in their use.

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Quantization Matrix Conversion for Scaled DCT Computations

Disclosed is a method for converting quantization
matrices derived for DCT (discrete cosine transform) compression of
data to matrices for use with scaled-DCT methods (which offer
significant computational savings) and a method for increasing the
accuracy in their use.

Scaled DCTs offer significant computational savings over
ordinary DCTs in such applications as compression of continuous tone
image data. However, most quantization matrices are designed for
implementation with DCTs. Hence, when a transmitter sends a code of a
compressed image file together with a quantization matrix Q obtained
in the usual DCT manner, in order to decompress the file using a
scaled-DCT algorithm, it is necessary to convert the matrix Q to a
matrix R for use with the inverse scaled-DCT.

The mathematical relation between the two quantization matrices
is given by
R = Q x D,
where x denotes the pointwise product and D is a fixed matrix, as
described in (*). The matrix D has some non-rational entries, and so
for integer implementation it is necessary to use some integer
approximation of this matrix. However, this approximation may prove
to be too coarse, as some of the entries in D are small real numbers
(for example, approximating !2 by its nearest integer, 1, yields more
than a 40 percent error).

It is proposed to multiply the entire quantization matrix by
some integer power of 2, say 2k; then approximat...