Image Denoising

1
?????? ????? ??????? ?????????
????????????????? ???????????
2
???? ? ??????? ?????
AWGN
Salt and pepper
????
????????????
??????????
?????????
Salt and pepper ?????? ? ?????
?????????? ????? ????? ??????
??? ?????? ? ?????
????? ??? ??????? ????????, ?? ??????????????
???? ? ?????? ???????/???????????/??????????? ???
????? ????????????? ???????? ???????? ??????????
??? ???????????? ? ??????? ??????????? ? ??
??????? ?? ????
3
?????? ??????????????
AWGN
Salt and pepper
????
????????????
??????????
?????????
????????? ?????? ?????????? ??????? ????????
???????
Bilateral filter Non-Local Means Wavelet
thresholding DCT, PCA, ICA ????????????
???????? ???????? BM3D
???????? ??????? ??????????????? ??????
4
?????????? ????

• ????????? ??????????
• ??????????? ??????? ???????????????? ???????
  ????????
• ??? ???? ? ???????? ??????????????

??????? 3?3
5
?????????? ????

• ????????? ??????????
• ??????????? ??????? ???????????????? ???????
  ????????
• ??? ???? ? ???????? ??????????????

??????? 7?7
6
?????????? ????

• ????????? ??????????
• ??????????? ??????? ???????????????? ???????
  ????????
• ??? ???? ? ???????? ??????????????

??????? 15?15
7
?????????? ????

• ?.?. ???????? ???? ????? ????? ????????, ?? ??
  ???? ??????????? ??? ???????????!
• ?????????????? ?????????? ???????? (??????????
  ?????? ?????? ???????? ??????????? ? ???
  ????????? ???????????)
• ?????????? ?????? ?????????? ????????

??????? 3?3
?????????? ???????
8
???????????? ????

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

9
Bilateral filter

• ?????????? ?????????
• Bilateral filter
• ?????????? ??????????
• ????????
• ? ??????

??????????????? ????????
???????????????? ????????
10
Bilateral filter

• Bilateral filter ?????????????? ??????????

(??? ??????? ??????? ????????)
11
Non-Local Means

• ?????????? ?????????
• Non-local means (NL-means) ???? ??????? ??
  ???????? ????? ??????, ? ?? ????????? ????????

?(xi,j) ???? ?????? ??????? xi,j
12
Non-Local Means

• ?????????? ?????
• ???????? ????????? ???????? ??????????? ?????,
  ??? bilateral filter

???? ?????? ??? q1 ? q2, ?? ?? ??? q3
??????????? ?? Buades et al 2005

13
Non-Local Means

• ??????????? ? ??????????
• ??????? ???????? ??????????????? ???????????
• ? ???????? ???????? ????? ???????
  ?????????????? ?????????
• ?????????? ?????? ???????????
• ????????????? ?????? MMX/SSE ??? ????????? ??????
• ????????? ??????????? ?? ????? ? ?????????? ?????
  ??????, ? ?? ????????? ????????
• ????????????? ??????? ????? ??????????? ?????? ?
  ??????????? ???????? ?????????? ????????? ??????

14
Non-Local Means

• ?????????? ? ?????
• ??????? ?????? ?????? ????? ????????? ?? ????????
  ????? (??????? ?? ???????????????-?????????)
• ??? ????????? ???????? ????? ????????? ?????????
  ?????? ?????? ?? Y-?????? ? ???????? ?????? YCrCb
  (YUV)

15
?????????? ?????

• ?????????? ?????????????? ??? ???????????
• DWT
• ?????? ?????? ? ??????? ????
• ?????????? ???????-????????????? (thresholding,
  shrinkage)
• ???????? DWT

?????????? ???? ?????????? ????????
?????????? ?????????????? ? ?????? ??????
??????????? ??????? ??? ????????? ??????

16
?????????????????? ??????

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

DFT
DCT
DST

?????? ???????????
??????????? ?? ??????? ????? ?????? ?????? ????
?????? ?????????? ?? ????????? ????

17
????? ??????? ?????????
Principal Component Analysis (PCA, KLT)

• ???? ??? ??????? ???????? ???????, ?????
  ??????????? ?????? ???????? ???????? ????? ????
  ????????? ??????? ?????????? ?????? ?? ??????????
  ??????.
• PCA ????????????? ???????? ??????????????
  ??????, ??? ??????? ?????? ?????? ?????? ??????
  ????????????? ??????????? ???????????? ?????????
  ??????, ?????? ?????? ?????????? ???????????
  ???????????? ????????? ? ?.?.

??????????? ?????? 2
18
????? ??????? ?????????
Principal Component Analysis (PCA, KLT)

• ??????? ???????? ??????? ??????????? ???????
  ei ??????? ?????????? Cx ???????? ?????? x
• ?????????????? ??????? ? ??????? ????????????
  ?????????? ??????? ???????? ??????

?? ??????? ??????????? n 2
19
??????????????
????? ??????? ?????????

• ?????????? ? ?????? ??????????? 8x8

64 ???????? ???????
20
??????????????
???????????? ??????? (Muresan/Parks, 2003)

• PCA-????????? ???????????
• ??????? ?????????????? PCA
• ?????????? ????????????? ? ????? ??????
• ???????? ?????????????? ? ????????? ?????? ?
  ???????????

????????? ? ??????? ??????????? (? ?.?. ?
?????? ?????? ???????)
??? ??????? ?????? ?????? ??????, ??? ?????????
?? ??????????? ??????? ???

21
??????????????
??????????
??????????? ???????????
?????????? ??????????????
22
??????????????
??????????
?????????????? ? ??????? PCA
????????????? ???? ?????