June 2014
Intermediate to advanced
576 pages
16h 43m
English
book
Image Analysis, Classification and Change Detection in Remote Sensing, 3rd Edition
by Morton J. Canty
Content preview from Image Analysis, Classification and Change Detection in Remote Sensing, 3rd Edition
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Exercises 157
multiplication of the column vector f
⊤
with the matrix
W =
h
0
h
1
h
2
h
3
0 0 0 0
h
3
−h
2
h
1
−h
0
0 0 0 0
0 0 h
0
h
1
h
2
h
3
0 0
0 0 h
3
−h
2
h
1
−h
0
0 0
0 0 0 0 h
0
h
1
h
2
h
3
0 0 0 0 h
3
−h
2
h
1
−h
0
h
2
h
3
0 0 0 0 h
0
h
1
h
1
−h
0
0 0 0 0 h
3
−h
2
.
(a) Prove that W is an orthonormal matrix (its inverse is equal to its
transpose).
(b) In the transformed vector W f
⊤
, the components of f
1
= Hf and
d
1
= Gf are interleaved. They can be sorted to give the vector (f
1
, d
1
).
When the matrix
W
1
=
h
0
h
1
h
2
h
3
h
3
−h
2
h
1
−h
0
h
2
h
3
h
0
h
1
h
1
−h
0
h
3
−h
2
is then applied to the smoothed vector (f
1
)
⊤
and the result again sorted,
we obtain the complete discrete wavelet transformation of f , namely
(f
2
, d
2
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