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Image and Video Compression
book

Image and Video Compression

by Madhuri A. Joshi, Mehul S. Raval, Yogesh H. Dandawate, Kalyani R. Joshi, Shilpa P. Metkar
November 2014
Intermediate to advanced content levelIntermediate to advanced
236 pages
7h 4m
English
CRC Press
Content preview from Image and Video Compression
53Image Transforms
This will allow yEyy x
H
|||
|[]||||
22
==
, where
||
||
is a norm:
yy
i
N
i
|
|||
2
0
1
2
=
=
Now the problem for optimal transform can be formulated as follows:
maxE
yy
H
.[ ]
s.t. yaxaaa
ai
j
iiii ij
,1
,0
;
**
==
=≠
Without going into the details of the proof for the above maximization prob-
lem, it can be shown that the energy for y can be maximized if
a
i
*
are the
eigenvectors of R
x
;
Ra
a
xi
ii
**
(i.e., transformation matrix A is formed using
the eigenvectors of the covariance matrix).
3.8 The Karhunen-Loeve Transform: Two-Dimensional
Image Transform with a Data-Dependent Basis
The Karhunen-Loeve transform (KLT) is also an example of the unitary ...
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Publisher Resources

ISBN: 9781482228229