RAW 4 E-mail: 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
4 4 2 RAW 4 4 4 (PCA) 4 4 4 4 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 3 4 3.1 RAW 1 4 RAW 4 G R B 2 4 1 4 4 4 4 4 4 GRBG RGGB BGGR GBRG 1 RAW 4 4 4 2
1 2 4 4 4 4 4 RAW RAW 4 4 RAW 3.2 4 4 G 1, R, B, G 2 4 RGB 4 1 4 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
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) 4. 3.3 4 4 RAW 4 RAW 4 4 1 (a) (b) (34.49dB). (35.28dB). 4 (σ = 20). RAW 4 3 4 GRBG RGGB BGGR GBRG 4 4 4 RAW 4 4 RAW 4 4 2 RAW RAW RAW (PSNR)
1 24 RAW PSNR[dB] ( ) σ [14] to CFA [7] [12] proposed 5 40.11 39.54 39.49 40.06 10 37.33 36.39 36.94 37.58 15 35.50 34.32 35.54 36.16 20 34.04 32.74 34.51 35.12 30 31.76 30.36 32.90 33.45 40 29.96 28.57 31.49 31.97 CPSNR [db] 40 38 36 34 32 30 Proposed [12] [10] [11] [14]toCFA [9] [7] 28 5 10 15 20 25 30 35 40 Noise level PSNR [db] 50 45 40 35 30 Proposed [12] [14]toCFA [7] 25 0 10 20 30 40 Noise sigma 5 PSNR. RAW RAW RAW CPSNR Kodak high resolution image dataset 24 2048 3072 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 2 6 24 CPSNR CPSNR BM3D [14] RAW CPSNR Park [12] 0.5dB 7 Park BM3D
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 5 34.84 38.76 38.48 38.99 39.01 39.48 39.13 39.07 39.52 10 29.35 35.38 35.81 36.80 36.67 36.97 36.38 36.78 37.32 15 26.01 32.92 34.16 35.40 35.26 35.17 34.49 35.41 35.99 20 23.63 30.99 32.93 34.35 34.12 33.68 33.01 34.46 34.98 30 20.32 28.10 31.01 32.62 N/A 31.33 30.74 32.81 33.35 40 18.04 26.00 29.47 31.12 N/A 29.46 29.00 31.41 31.89 [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 3971065, 1976. [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. 2167 2178, 2005. [3] X. Li, B. Gunturk, and L. Zhang, Image Demosaicing: A Systematic Survey, Proc. SPIE Electronic Imaging, vol. 6822, pp. 68221, 2008. [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. 023016 023016, 2011. [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. 2304 2308, 2013. [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.
125 129, 2009. [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. 797 812, 2009. [8] K. Hirakawa, and T.W. Parks, Joint demosaicing and denoising Image Processing, IEEE Trans. on Image Processing, vol. 15, no. 8, pp. 2146 2157, 2006. [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. 105 122, 2007. [10] L. Condat, and S. Mosaddegh, Joint demosaicking and denoising by total variation minimization, Proc. of IEEE Int. Conf. on Image Processing (ICIP), pp. 2781 2784, 2012. [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. 146 156, 2013. [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. 860 864, 2009. [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.2272 2279, 2009. [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.