??????(Discrete Wavelet Transformation, DWT)?DCT??,??????????????????????

1
??????

1. ??????(Discrete Wavelet Transformation,
   DWT)?DCT??,??????????????????????

2

• ????
• ??????????
• ???????????
• ???????????
• ??????????,?????????

3

• ????
• ??????????
• ???????????
• ????????
• ??????????,???????????

4

• ????Haar?????????
• Harr?????????????????????????,???????,??????????
  ?????????????????????????????????????????????????
  ???????????

5

• Harr??????????
• ??????????

A B C D AB CD A-B C-D
L L H H
(0,0) (0,1) (0,2) (0,3) (0,0) (0,1) (0,2) (0,3)
(1,0) (1,1) (1,2) (1,3) (1,0) (1,1) (1,2) (1,3)
(2,0) (2,1) (2,2) (2,3) (2,0) (2,1) (2,2) (2,3)
(3,0) (3,1) (3,2) (3,3) (3,0) (3,1) (3,2) (3,3)
Harr??????????????????O
????O
6

• ??????????

A C AB CD
B D LL LL HL HL
L L H H A-B C-D
L L H H LH LH HH HH
LL
HL
(0,0) (0,1) (0,2) (0,3) (0,0) (0,1) (0,2) (0,3)
(1,0) (1,1) (1,2) (1,3) (1,0) (1,1) (1,2) (1,3)
(2,0) (2,1) (2,2) (2,3) (2,0) (2,1) (2,2) (2,3)
(3,0) (3,1) (3,2) (3,3) (3,0) (3,1) (3,2) (3,3)
LH
HH
L
H
Harr??????????????????O
????O
7

• ??????????????????,?????????????????????LL?LH?H
  L?HH??????????????,??????????(subband)??LL??????
  ???????,?????LL????????????????????????,?????????
  ,???????????,???????????????????????????????????
  ?????n??????????????????,???????????????????,?????
  ????

8
LL1 HL1 LL2 HL2 HL1
LL1 HL1 LH2 HH2 HL1
LH1 HH1 LH1 LH1 HH1
???
???
LL3 HL3 HL2 HL1
LH3 HH3 HL2 HL1
LH2 LH2 HH2 HL1
LH1 LH1 LH1 HH1
????????
???
??Harr??????????
9
20 15 30 20 35 50 5 10
17 16 31 22 33 53 1 9
15 18 17 25 33 42 -3 -8
21 22 19 18 43 37 -1 1
????O
??????????O
68 103 6 19 326 -38 6 19
76 79 -4 -7 16 -32 2 -7
2 -3 4 1 2 -3 4 1
-10 5 -2 -9 -10 5 -2 -9
???????????? (?????????????)
??????????O
10

• ?????????????
• ???????????????,?scan order??????????????????scan
  order???????????,?????,???????????????????,?????
  ?????????,??????????????????????

11
scan order???????
LL3 HL3 HL2 HL1
LH3 HH3 HL2 HL1
LH2 LH2 HH2 HL1
LH1 LH1 LH1 HH1
scan order???????
12




scan order??????????
13

• ?????????????
• ???????????,????????????????????????,????????quad
  tree????????root,quadtree????????????????????????
  ???,??????????????????????

14

X

Y



LL2
HL2
HL1
LH2
HL1
HH1
(a)????????????
15
X


Y



LL2
X
LH2
Y
LH1
(b)?(a)????quadtree??
16

• ????????(Haar)
• ??????(Continuous WT, CWT)?

17

• ?(a, ?)?????,??a a0m,? n?0a0m,??m?n???,???????
  ???