Chip Design Magazine::
My focus was. Usually, they consist of a reconfigurable matrix and a host processor, The parser and abstraction steps transform the architecture into an be mentioned that basic array components can be more efficiently used. . In 1996, he started IMEC's Multimedia Image Compression Systems group.
http://www.chipdesignmag.com/display.php?articleId=950&issueId=19HOME |
Dear all,
I want to design a my own transform basis matrix.
For 2D case, forward transform is: Y=A*X*B, inverse transform is:
Z=C*Y*D... let's say X, Y, Z, A, B, C, D are 8x8 matrices...
Can anybody tell me what relationship should A, B, C, D have?
1)Orthognality?
2)A=B'?
3)C=D'?
4)A=B^(-1)?
5)C=D^(-1)?
6)B=C?
7)A=D?
...
Thank you very much if you can also point me to some resources for
reference?
Thanks a lot,
-Mizhael
Hi!!
I need some clarifications:
When you say "let's say X, Y, Z, A, B, C, D are 8x8 matrices", are
these matrices satisfies both equations:
Y=A*X*B
Z=C*Y*D ?
In the affirmative, the answers does not depend on the "size" of the
matrices, the answer will be general for nxn matrices. So why you are
asking specifically for 8x8 matrices?
What "For 2D case" means?
What A' means? (please clarify the notation, is it the transposed
matrix?)
Thank you.
livioflores-ga Compression Links: Burrows-Wheeler Transform/Block Sorting area::
The abstract says that compression can be improved by alphabet ordering . The Delphi source is available for download from the web site and can be used under his own APL. . compression to my Visual Basic project and it worked like a charm. . Sebastian talks about some alternatives that help compression.
http://compression-links.info/BWTHOME |
Sufficient conditions are
C=A ^ (-1)
B=D ^ (-1)
Derivation:
Z= C * Y * D = C * A * X * B * D
When conditions are satisfied, C*A=I and B*D =I
therefore Z= I * X * I = X, so that transform is inverse.
I is unit matrix here.
References:
for matrix calculations in general
http://www.math.duke.edu/education/ccp/materials/linalg/index.html
and
http://www.numbertheory.org/book/
Mathematics for image compression
http://home.olemiss.edu/~lcao/bm_content.html
Image compression - techniques
http://academic.mu.edu/phys/matthysd/web226/L0423.htm
for advanced techniques:
http://www.geoffdavis.net/dartmouth/wavelet/wavelet.html
SEARCH TERMS
none for the question,
for references:
matrix algebra
2D linear filters
mathematics , image compression
linear algebra tutorial
hedgie
Hey, Hedgie,
Yeah, image compression is the direction. The thing is that I cannot
use any A and D, right? There must be some properties that A and D
should meet, right?
I saw most books talk about orthonomal/orthogonal matrix for A. But
why? I know orthogonality/unitarility can simplify the design, but is
that absolutely neccesary?
Given A is orthogonal, how do you design this 8x8 matrix? DCT2D is a
good option, but do we have others?
Given A is not orthogonal, how to design this matrix? from a11, a12,
a13, to... a88, then what are the B, C, D's?
Again, this is for image compression, having a quantization after the
transform... AN OPTIMIZED VECTOR QUANTIZATION FOR COLOR IMAGE COMPRESSION ::
File Format: PDF/Adobe Acrobat - View as HTMLAny image compression technique can be modeled to be a three-stage process Decomposition of an image by wavelet transform using orthogonal basis .. Define the matrix E to be the transformation matrix in Equation 4.9. .. Center, I agree that the Library and my major department shall make it freely
http://etd.lib.ttu.edu/theses/available/etd-01072009-31295012443478/unrestricted/31295012443478.pdfHOME |
hi mizhael
Nice overview of the Image compression is here
http://www.acm.org/crossroads/xrds6-3/sahaimgcoding.html
It covers the older DCT and evolution to the newer DWT.
I would need more context if additional clarification is needed.
hedgie
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HELP! How can I design my own transform basis matrix for image compression?