4 4 2 RAW (PCA) RAW RAW [5] 4 RAW 4 Park [12] Park 2 RAW RAW 2 RAW y = Mx + n. (1) y RAW x RGB M CFA n.. R G B σr 2, σ2 G, σ2 B D n ( )
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1 RAW 4 hakiyama@ok.ctrl.titech.ac.jp Abstract RAW RAW RAW RAW RAW 4 RAW RAW RAW 1 (CFA) CFA Bayer CFA [1] RAW CFA 1 2 [2, 3, 4, 5]. RAW RAW RAW RAW 3 [2, 3, 4, 5] (AWGN) [13, 14] RAW 2 RAW RAW RAW RAW [6, 7, 12] 3 [8, 9, 10, 11] RAW RAW RAW 4 G 2 4
2 4 4 2 RAW (PCA) RAW RAW [5] 4 RAW 4 Park [12] Park 2 RAW RAW 2 RAW y = Mx + n. (1) y RAW x RGB M CFA n.. R G B σr 2, σ2 G, σ2 B D n ( ) D m ( ) ˆx = D n (D m (Mx + n)). (2). η = D m (Mx + n) x. (3) ˆx = D m (D n (Mx + n)). (4) RAW RAW RAW RAW RAW 1 4 RAW 4 G R B GRBG RGGB BGGR GBRG 1 RAW
3 RAW RAW 4 4 RAW G 1, R, B, G 2 4 RGB Park RGB RGB 4 4 [12] RAW [7] 4 [ ] X = x 1 + n 1 x 2 + n 2 x m + n m, (5) Σ = 1 m 1 ( X µ 1 T m)( X µ 1 T m) T, (6) µ = 1 m m x i. (7) i=1 x i i 4 n i i m 4 1 m 1 m T Σ = Σ diag ( [ σ 2 Y 1 σ 2 Y 2 σ 2 Y 3 σ 2 Y 4 ] T ). (8) diag(z i ) z i σ 2 k 4 k GRBG
4 3 Y 1 G 1 Y 2 Y 3 = P R B, (9) Y 4 G 2 P 11 P 12 P 13 P 14 P = P 21 P 22 P 23 P 24 P 31 P 32 P 33 P 34. (10) P 41 P 42 P 43 P 44 P Σ v k. [ ] T P = v 1 v 2 v 3 v 4. (11) P 4. k σ 2 Y k = P 2 1kσ 2 G + P 2 2kσ 2 R + P 2 3kσ 2 B + P 2 4kσ 2 G. (12) RAW 4 RAW (a) (b) (34.49dB). (35.28dB). 4 (σ = 20). RAW GRBG RGGB BGGR GBRG RAW 4 4 RAW RAW RAW RAW (PSNR)
5 1 24 RAW PSNR[dB] ( ) σ [14] to CFA [7] [12] proposed CPSNR [db] Proposed [12] [10] [11] [14]toCFA [9] [7] Noise level PSNR [db] Proposed [12] [14]toCFA [7] Noise sigma 5 PSNR. RAW RAW RAW CPSNR Kodak high resolution image dataset RAW RAW 0 RAW [14] [5] 4.1 RAW RAW BM3D [14] RAW PCASAD [7] Park [12] BM3D [14] RAW 6 CPSNR. RAW BM3D Park BM3D 1 5 Kodak dataset 24 PSNR PSNR 4.2 RAW CFA [5] LPAICI [9], JDDTV [10], LSLCD [11] RAW CPSNR CPSNR BM3D [14] RAW CPSNR Park [12] 0.5dB 7 Park BM3D
6 2 24 CPSNR[dB] ( ) Type Dm Dm Dn Joint Dn and Dm Dn Dm [5] σ [5] [5] + [14] [9] [10] [11] [14]toCFA [7] [12] proposed N/A N/A [11] σ = 20. (a) ground truth (b) [5] (c) [5]+[14] (d) [9] (e) [10] (f) [11] (g) [14]toCFA (h) [7] (i) [12] (j) proposed 7 Kodak high resolution image dataset (σ = 20). Park [12] 5 RAW RAW 4 RAW [1] B. Bayer, Color imaging array, U.S. Patent , [2] L. Zhang and X. Wu, Color demosaicking via directional linear minimum mean square-error estimation, IEEE Trans. on Image Processing, vol. 14, no. 12, pp , [3] X. Li, B. Gunturk, and L. Zhang, Image Demosaicing: A Systematic Survey, Proc. SPIE Electronic Imaging, vol. 6822, pp , [4] L. Zhang, X. Wu, A. Buades, and X. Li, Color demosaicking by local directional interpolation and nonlocal adaptive thresholding, Journal of Electronic Imaging, vol. 20, no. 2, pp , [5] D. Kiku, Y. Monno, M. Tanaka, and M. Okutomi, Residual Interpolation for Color Image Demosaicking, Proc. of IEEE Int. Conf. on Image Processing (ICIP), pp , [6] A. Danielyan, M. Vehvilainen, A. Foi, V. Katkovnik, and K. Egiazarian Cross-color BM3D filtering of noisy raw data, in Proc. International Workshop on Local and Non-Local Approximation in Image Processing LNLA, pp.
7 , [7] L. Zhang, R. Lukac, X. Wu, and D. Zhang, PCA-based spatially adaptive denoising of CFA images for single-sensor digital cameras, IEEE Trans. on Image Processing, vol. 18, no. 4, pp , [8] K. Hirakawa, and T.W. Parks, Joint demosaicing and denoising Image Processing, IEEE Trans. on Image Processing, vol. 15, no. 8, pp , [9] D. Paliy, V. Katkovnik, R. Bilcu, S. Alenius, and K. Egiazarian, Spatially Adaptive Color Filter Array Interpolation for Noiseless and Noisy Data, Int. J. Imaging Sys. Tech., Sp. Iss. Appl. Color Image Process., vol. 17, no. 3, pp , [10] L. Condat, and S. Mosaddegh, Joint demosaicking and denoising by total variation minimization, Proc. of IEEE Int. Conf. on Image Processing (ICIP), pp , [11] E. Dubois, and G. Jeon, Demosaicking of Noisy Bayer-Sampled Color Images With Least-Squares Luma-Chroma Demultiplexing and Noise Level Estimation, IEEE Trans. on Image Processing, vol. 22, no. 1, pp , [12] S. H. Park, H. S. Kim, S. Lansel, M. Parmar, and B. A. Wandell, A case for denoising before demosaicking color filter array data Asilomar Conf. on Signals, Systems, and Computers, pp , [13] J. Mairal, F. Bach, J. Ponce, G. Sapiro, and A. Zisserman, Non-local sparse models for image restoration. IEEE Int. Conf. on Computer Vision (ICCV), pp , [14] K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, Image denoising with block-matching and 3D filtering, Proc. SPIE Electronic Imaging, no. 6064A 30, 2006.
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