Databases Reference
In-Depth Information
and R.E. Wood [96]. This topic has an especially nice discussion of the Hotelling trans-
form.
5.
The bit allocation problem and its solutions are described in
Vector Quantization and
Signal Compression
, by A. Gersho and R.M. Gray [
136
].
6.
A very readable description of transform coding of images is presented in
Digital Image
Compression Techniques
, by M. Rabbani and P.W. Jones [
91
].
7.
The Data Compression Book
, byM. Nelson and J.-L. Gailly [
69
], provides a very readable
discussion of the JPEG algorithm.
13.9 Projects and Problems
1.
A square matrix
A
has the property that
A
T
A
AA
T
=
=
I
, where
I
is the identity matrix.
If
X
1
and
X
2
are two
N
-dimensional vectors and
1
=
A
X
1
2
=
A
X
2
then show that
2
2
|
X
1
−
X
2
|
= |
1
−
2
|
(73)
2.
Consider the following sequence of values:
10
11
12
11
12
13
12
11
10
−
10
8
−
7
8
−
8
7
−
7
(a)
Transform each row separately using an eight-point DCT. Plot the resulting 16
transform coefficients.
(b)
Combine all 16 numbers into a single vector, and transform it using a 16-point DCT.
Plot the 16 transform coefficients.
(c)
Compare the results of (a) and (b). For this particular case would you suggest a
block size of 8 or 16 for greater compression? Justify your answer.
3.
Consider the following “image”:
4321
3211
2111
1111
(a)
Obtain the two-dimensional DWHT transform by first taking the one-dimensional
transform of the rows, then taking the column-by-column transform of the resulting
matrix.
