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p (" X) = # ( ) p " p X " ( ) p( X ")p(")dx X( ;( ˆ " = " # p " X ( )d" ˆ " = argmax " p (" X) ˆ " = argmax " p( X ") 5
p (" X) = # ( ) p " p X " ( ) p( X ")p(")dx X( ;( <. =. >. 6
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?%9*76&@%87/ p (" X) = # ( ) p " p X " ( ) p( X ")p(")dx X( ( ( ) = p x i # i p X " $ i ( ) p " % i % j$n( i) ( ) ( ) = p # i,# j 8
p X " $ i ( ) ( ) = p x i # i p " % i % j$n( i) ( ) ( ) = p # i,# j?&"'c7d"e0"6*- 9
FGH 10
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IIG IJKL > < M?KNOKPQ> 12
IIG IIG =R<R << STI<=(>U 13
IJKL IJKL =R<R << STI<=(> 14
> HVAVW I?X 15 " " # # # # # # " " # # # " # " # " # " # "##$%&'( "##$%&') "##$%&'* "##$%&'+
Output Input 16
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6%1 C96%1 http://www.cybercom.net/~dcoffin/dcraw/ W&'&/"%6 NPA ^^A XFG _#`arb>cd <[2&* '&/"%6IH? _#Yd I?X 18
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IJKL 21
IIG =R<R << =e STIe(=U 22
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I = A( I + N s + N DC + N ) R I( ( N S I A( N S ( N DC ( N R ( I = f A( I + N s + N DC + N ) R ( ) + N Q Glenn E. Healey and Raghava Kondepudy, Radiometric CCD Camera Calibration and Noise Estimation, PAMI, Vol. 16, No. 3, pp. 267-274, 1994 24
I = A( I + N s + N DC + N ) R I = AtP + AtE( N ) DC " 2 = A 2 tp + A 2 2 t" DC + A 2 " R 2 " 2 = s I + t 76 25
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HAW HAW 27
HAW " 2 = s I + t I R I B " p I % R $ ' = p ( I # & )p " K % ( $ # I ' di, K = I R & I B f(x) = 1/x I B 28
_IIGd _IJKLd IIG IJKL 29
<. =. >. Y. Z. [. U. X5G \.
" 2 I ( i) = $ 2 w j " O ( ) j#n i ( j) # # # # " " " # # " # # " # # "##$%&'( " # "##$%&'* Jun Takamatsu, Yasuyuki Matsushita, Tsukasa Ogasawara and Katsushi Ikeuchi, Estimating demosaicing algorithms using image noise variance, CVPR, 2010 31
O = f ( I) ( ) = p( I) f '( I) p O " 2 O # f '( I) ( ) 2 " I 2 $ p( I I )di " 2 O = ( I # µ ) 2 O Jun Takamatsu, Yasuyuki Matsushita and Katsushi Ikeuchi, Estimating radiometric response functions from image noise variance, ECCV, 2008 32
X5G [a i,b i ) "i # Z " O 2 = " I 2 + q2 12 q 1 " 2 Q = * x 2 q dx = 1 2 q ) q 2 # % $ x 3 3 & ( ' q 2 ) q 2 = q2 12 33
i j^oa \E\ 34
35
36
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^7&/*A6"fG6%g7/hfH#I3%//"' <RR 38
( ) = A( K p ( ) + N ( s p) + N ( DC p) + N ) R + N Q I p ( ) I p " N 2 p ( ( )) +" 2 C ( ) # A 2 I + E N ( DC p) " N 2 p ( ( ( ))) µ = A I + E N DC p ( ) " C 2 kx " C 2 = A 2 " R 2 + q2 12 Glenn E. Healey and Raghava Kondepudy, Radiometric CCD Camera Calibration and Noise Estimation, PAMI, Vol. 16, No. 3, pp. 267-274, 1994 39
( ) = A N ( DC p) + N R I p ( ) + N Q ( ) = AE( N ( DC p) ) E I( p) E I ( i p) ( ) = A K p ( ( ) I ( p ) + E( N ( i DC p) )) ( ) E N ( DC p) 40
P&+7/G>LlLK\RR <5ZR C96%1b3#Y 97/m"6*#C"0*3\ \2&* " # X R.RUe R.R<Y R.RRee n 9= R.=> R.R>< R.<\ # # # " " # # # " " # # # # "## " "## 41
_ZRRR d " # R.eeeZ R.eeeZ R.eeeZ R.R>=< R.R><[ R.R><e IIG <R 42
" # R.R[\ R.R<R R.R<Z <.< R.>Y R.YU 43
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T7*%'N%6&%87/ ]&"/"6?&'*"6 ]%m"'"*t36"-37'c&/g P7/#'79%'_Po#$"%/-VOE%$0'" VWJ>Gd A. Buades, B. Coll, and J. M. Morel, A review of image denoising algorithms, with a new one, Multiscale Modeling and Simulation, Vol. 4, No. 2, pp. 490-530, 2005. 45
46
P7/o79%' Kostadin Dabov, Alessandro Foi, Vladimir Katkovnik, and Karen Egiazarian, Image Denoising by Sparse 3D Transform-domain Collaborative Filtering, IEEE Trans on Image Processing, Vol. 16, No. pp. 2080-2095, 2007 47
G6%g7/hfH#I3%//"'VWJ>G 6 x 10-5 5 4 3 2 1 0 0 0.2 0.4 0.6 0.8 1 48
Ce Liu, William T. Freeman, Richard Szeliski and Sing Bing Kang, Noise Estimation from a Single Image, CVPR, 2006. 49
50
I = At( P + E( N )) DC k ( ) = At 1 P + E( N ) DC g O 1 g O 2 ( ) ( ) ( ) = At 2 P + E( N ) DC ( ) ( ) = t 1 g O 1 g O 2 t 2 51
f ( I) = I " f ( I) = "I # + $ f ( I) = I P I, { " i } f ( I) = w i I i " i=1 ^6&76M^IX http://www.cs.columbia.edu/cave/software/softlib/dorf.php ( ),P I, " i ( { }) = " i I i # i=0 52
N&g/"p/g K089%'C"/-&*f " 1 % Optical density = log 10 $ ' # Light Transmission& 1 Light Transmission = pow(10, Optical density) 53
FGH =R<R << =e STIe(YR HDR " 2 = A 2 tp + A 2 2 t" DC + A 2 " R 2 +" Q 2 I = At( P + E( N DC )) Samuel W. Hasinoff, Fredo Durand and William T. Freeman, Noise-Optimal Capture for High Dynamic Range Photography, CVPR, 2010. t 2 P 2 SNR 2 = 2 tp + t" DC +" 2 R + 1 A " 2 2 Q 54
Li Zhang, Alok Deshpande and Xin Chen, Denoising vs. Deblurring: HDR Imaging Techniques Using Moving Camera, CVPR, 2010 55
$ %$ $% 56
V n = 4kTR"f k( "f( af@c T( R( 57
HX] " 2 = A 2 tp + A 2 2 t" DC + A 2 " R 2 X5G i 58
Yasuyuki Matsushita and Stephen Lin, Radiometric Calibration from Noise Distributions, CVPR, 2007. 59
Noise variance# Imaging process# Output# Response f Noise variance# Observation# Input# Radiometric Calibration# Inverse response g Noise variance# Input Input# Output# Output# Input# Jun Takamatsu, Yasuyuki Matsushita and Katsushi Ikeuchi, Estimating radiometric response functions from image noise variance, ECCV, 2008
I?X I?X Jun Takamatsu, Yasuyuki Matsushita, Tsukasa Ogasawara and Katsushi Ikeuchi, Estimating demosaicing algorithms using image noise variance, CVPR, 2010 61
$ %$&'()'*$+'(,-'. %$ 62
IH? 63
IH? ( ) R xx R x 2 = R xy R x R y ( ) = R yy R = f '' f "1 R 2 y f '( f "1 ( R) ) 2 Yu-Feng Hsu and Shih-Fu Chang, Image Splicing Detection using Camera Response Function Consistency and Automatic Segmentation, Int. Conf. on Multimedia Expo., pp. 28-31, 2007 Zhouchen Lin, Rongrong Wang, Xiaoou Tang and Heung-Yeung Shum, Detecting Doctored Images Using Camera Response Normality and Consistency, CVPR, 2005 64
koj Alin C. Popescu and Hany Farid, Exposing Digital Forgeries in Color Filter Array Interpolated Images, IEEE Transactions on Signal Processing, Vol. 52, No. 10, pp. 3948 3959, 2005 65
G%B2"93&"-1%m"'"* Jan Lukas, Jessica Fridrich and Miroslav Goljan, Digital Camera Identification from Sensor Pattern Noise, IEEE Trans. on Information Forensics and Security, Vol. 1, No. 2, pp. 205-214, 2006. Mo Chen, Jessica Fridrich, Miroslav Goljan and Jan Lukas, Determining Image Origin and Integrity Using Sensor Noise, IEEE Trans. on Information Forensics and Security, Vol. 3, No. 1, pp. 74-90, 2008. 66
^IX, MIRU 2010 67
68
ˆ " = argmin " $ i ( y i # f ( x i ;")) 2 k 69
y = f (x;") + e p( y i x i,") = ( ) 1 & 2#$ exp y % f x i i 2 ( ' 2$ 2 ) + * ( { }) = p { y i} x i p " { x i }, y i & ( { },") = 1, 2#$ exp ( % y % f x i i 2 ( 2$ 2 i ' ( ) ( ) 2 ) + + * "log p ({ y i }{ x i },#) = $ y i " f x i i ( ) ( ) 2 + const 70
k 71
"" i j A F = a ij 2 72
J#"-8$%*76VHXPLXI HXPLXI =R<R << =e STI<R(RZ 73
o0# # x p = % $ n " i=1 x i p & ( ' x " = max x 1,, x n ( ) x 2 = x 1 2 ++ x n 2 x 1 = x 0 = x 1 ++ x n R $ 1"# ( x i ) i L1-Lasso, Fixed point algorithm Marching pursuit 74
G( minrank( A) + " E 0 s.t. D = A + E o<#6"'%e%87/ min A * + " E 1 s.t. D = A + E John Wright, Arvind Ganesh, Shankar Rao, Yigang Peng, and Yi Ma, Robust principal component analysis: exact recovery of corrupted low-rank matrices via convex optimization, NIPS, 2009 75
o= o0 p( x) = % " % % 2#$ ' & 1 exp + x + µ ( ' * ( * ' & # ) ") & p ( * ) or I7$06"--"C-"/-&/gi k 76
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( Christopher M. Harris and Daniel M. Wolpert, Signal-dependent noise determines motor planning, Nature, Vol. 394, pp. 780-784, 1998. 78
FGH 79
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T3%/+f7BD76f7B6+&/C%4"/87/q 81