Abstract

A novel, speckle noise reduction algorithm based on the combination of Anisotropic Diffusion (AD) filtering and Interval Type-II fuzzy sets was developed for reducing speckle noise in Optical Coherence Tomography (OCT) images. Unlike regular AD, the new Type-II fuzzy AD algorithm considers the uncertainty in the calculated diffusion coefficient and appropriate adjustments to the coefficient are made. The new algorithm offers flexibility in optimizing the trade-off between two of the image metrics: signal-to-noise (SNR) and Edginess, which are directly related to the structure of the imaged object. Application of the Type-II fuzzy AD algorithm to OCT tomograms acquired in-vivo from a human finger tip and human retina show reduction in the speckle noise with very little edge blurring and about 13 dB and 7 dB image SNR improvement respectively. Comparison with Wiener, Adaptive Lee and regular AD filters, applied to the same images, demonstrates the superior performance of the Type-II fuzzy AD algorithm in terms image SNR and edge preservation metrics improvement.

© 2009 Optical Society of America

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2008

2007

A. E. Desjardins, B. J. Vakoc, W. Y. Oh, S. M. R. Motaghiannezam, G. J. Tearney, and B. E. Bouma, "Angle-resolved Optical Coherence Tomography with sequential angular selectivity for speckle reduction," Opt. Express 15, 6200-6209 (2007).
[CrossRef] [PubMed]

H. M. Salinas and D. C. Fernandez, "Comparison of pde-based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography," IEEE Trans. Med. Imaging 26, 761-771 (2007).
[CrossRef] [PubMed]

P. Puvanathasan and K. Bizheva, "Speckle noise reduction algorithm for optical coherence tomography based on interval type II fuzzy set," Opt. Express  15, 15747-15758 (2007).
[CrossRef] [PubMed]

A. Ozcan, A. Bilenca, A. E. Desjardins, B. E. Bouma, and G. J. Tearney, "Speckle reduction in optical coherence tomography images using digital filtering," J. Opt. Soc. Am. A. 24, 1901-1910 (2007).
[CrossRef]

2005

J. Kim, D. T. Miller, E. Kim, S. Oh, J. Oh, and T. E. Milner, "Optical coherence tomography speckle reduction by a partially spatially coherent source," J. Biomed. Opt. 10, 64034 -9 (2005).
[CrossRef]

D. C. Fernandez and H. M. Salinas, "Evaluation of a nonlinear diffusion process for segmentation and quantification of lesions in optical coherence tomography images," Proc. SPIE 5747, 1834-1843 (2005).
[CrossRef]

D. C. Fernandez, H. M. Salinas and C. A. Puliafito, "Automated detection of retinal layer structures on optical coherence tomography images," Opt. Express 13, 10200-10216 (2005).
[CrossRef]

R. K. Wang, "Reduction of speckle noise for optical coherence tomography by the use of nonlinear anisotropic diffusion," Proc. SPIE 5690, 380-385 (2005).
[CrossRef]

2004

2003

M. Pircher, E. Götzinger, R. Leitgeb, A.F. Fercher, and C. K. Hitzenberger, "Speckle reduction in optical coherence tomography by frequency compounding," J. Biomed. Opt. 8, 565-569 (2003).
[CrossRef] [PubMed]

N. Iftimia, B. E. Bouma, and G. J. Tearney, "Speckle reduction in optical coherence tomography by path length encoded angular compounding," J. Bio. Opt. 8, 260-263 (2003).
[CrossRef]

2000

J. Rogowska and M. E. Brezinski, "Evaluation of the adaptive speckle suppression filter for coronary optical coherence tomography imaging," IEEE Trans. Med. Imaging 19, 1261-1266 (2000).
[CrossRef]

1999

J. M. Schmitt, S. H. Xiang, and K. M. Yung, "Speckle in optical coherence tomography," J. Bio. Opt. 4, 95-105 (1999).
[CrossRef]

1992

G. Gerig, O. Kubler, R. Kikinis, and F. A. Jolesz, "Nonlinear anisotropic filtering of mri data," IEEE Trans. Med. Imaging 11, 221-232 (1992).
[CrossRef] [PubMed]

F. Catte, P. L. Lions, J. M. Morel, and T. Coll, "Image selective smoothing and edge detection by nonlinear diffusion," SIAM J. Numer. Anal. 29, 182-193 (1992).
[CrossRef]

1990

P. Perona and J. Malik, "Scale-space and edge detection using anisotropic diffusion," IEEE Trans. Pattern Anal. and Mach. Intell. 12, 629-639 (1990).
[CrossRef]

1984

J. Koenderink, "The structure of images," Biol. Cybern. 50, 363-370 (1984).
[CrossRef] [PubMed]

1965

L. A. Zadeh, "Fuzzy sets," Information Control 8, 338-353 (1965).
[CrossRef]

Adler, D. C.

Aja, S.

S. Aja, C. Alberola, and J. Ruiz, "Fuzzy anisotropic diffusion for speckle filtering," in IEEE Int. Conf. Acoust. Speech Signal Process.  2, 1261-1264 (2001).

Alberola, C.

S. Aja, C. Alberola, and J. Ruiz, "Fuzzy anisotropic diffusion for speckle filtering," in IEEE Int. Conf. Acoust. Speech Signal Process.  2, 1261-1264 (2001).

Bilenca, A.

A. Ozcan, A. Bilenca, A. E. Desjardins, B. E. Bouma, and G. J. Tearney, "Speckle reduction in optical coherence tomography images using digital filtering," J. Opt. Soc. Am. A. 24, 1901-1910 (2007).
[CrossRef]

Bizheva, K.

Bouma, B. E.

A. Ozcan, A. Bilenca, A. E. Desjardins, B. E. Bouma, and G. J. Tearney, "Speckle reduction in optical coherence tomography images using digital filtering," J. Opt. Soc. Am. A. 24, 1901-1910 (2007).
[CrossRef]

A. E. Desjardins, B. J. Vakoc, W. Y. Oh, S. M. R. Motaghiannezam, G. J. Tearney, and B. E. Bouma, "Angle-resolved Optical Coherence Tomography with sequential angular selectivity for speckle reduction," Opt. Express 15, 6200-6209 (2007).
[CrossRef] [PubMed]

N. Iftimia, B. E. Bouma, and G. J. Tearney, "Speckle reduction in optical coherence tomography by path length encoded angular compounding," J. Bio. Opt. 8, 260-263 (2003).
[CrossRef]

Boyd, S.

Brezinski, M. E.

J. Rogowska and M. E. Brezinski, "Evaluation of the adaptive speckle suppression filter for coronary optical coherence tomography imaging," IEEE Trans. Med. Imaging 19, 1261-1266 (2000).
[CrossRef]

Catte, F.

F. Catte, P. L. Lions, J. M. Morel, and T. Coll, "Image selective smoothing and edge detection by nonlinear diffusion," SIAM J. Numer. Anal. 29, 182-193 (1992).
[CrossRef]

Coll, T.

F. Catte, P. L. Lions, J. M. Morel, and T. Coll, "Image selective smoothing and edge detection by nonlinear diffusion," SIAM J. Numer. Anal. 29, 182-193 (1992).
[CrossRef]

Desjardins, A. E.

A. Ozcan, A. Bilenca, A. E. Desjardins, B. E. Bouma, and G. J. Tearney, "Speckle reduction in optical coherence tomography images using digital filtering," J. Opt. Soc. Am. A. 24, 1901-1910 (2007).
[CrossRef]

A. E. Desjardins, B. J. Vakoc, W. Y. Oh, S. M. R. Motaghiannezam, G. J. Tearney, and B. E. Bouma, "Angle-resolved Optical Coherence Tomography with sequential angular selectivity for speckle reduction," Opt. Express 15, 6200-6209 (2007).
[CrossRef] [PubMed]

Drexler, W.

W. Drexler, "Ultrahigh-resolution optical coherence tomography," J. Bio. Opt. 9, 47-74 (2004).
[CrossRef]

Fercher, A.F.

M. Pircher, E. Götzinger, R. Leitgeb, A.F. Fercher, and C. K. Hitzenberger, "Speckle reduction in optical coherence tomography by frequency compounding," J. Biomed. Opt. 8, 565-569 (2003).
[CrossRef] [PubMed]

Fernandez, D. C.

H. M. Salinas and D. C. Fernandez, "Comparison of pde-based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography," IEEE Trans. Med. Imaging 26, 761-771 (2007).
[CrossRef] [PubMed]

D. C. Fernandez and H. M. Salinas, "Evaluation of a nonlinear diffusion process for segmentation and quantification of lesions in optical coherence tomography images," Proc. SPIE 5747, 1834-1843 (2005).
[CrossRef]

D. C. Fernandez, H. M. Salinas and C. A. Puliafito, "Automated detection of retinal layer structures on optical coherence tomography images," Opt. Express 13, 10200-10216 (2005).
[CrossRef]

Forbes, P.

Fujimoto, J. G.

Gerig, G.

G. Gerig, O. Kubler, R. Kikinis, and F. A. Jolesz, "Nonlinear anisotropic filtering of mri data," IEEE Trans. Med. Imaging 11, 221-232 (1992).
[CrossRef] [PubMed]

Götzinger, E.

M. Pircher, E. Götzinger, R. Leitgeb, A.F. Fercher, and C. K. Hitzenberger, "Speckle reduction in optical coherence tomography by frequency compounding," J. Biomed. Opt. 8, 565-569 (2003).
[CrossRef] [PubMed]

Hitzenberger, C. K.

M. Pircher, E. Götzinger, R. Leitgeb, A.F. Fercher, and C. K. Hitzenberger, "Speckle reduction in optical coherence tomography by frequency compounding," J. Biomed. Opt. 8, 565-569 (2003).
[CrossRef] [PubMed]

Iftimia, N.

N. Iftimia, B. E. Bouma, and G. J. Tearney, "Speckle reduction in optical coherence tomography by path length encoded angular compounding," J. Bio. Opt. 8, 260-263 (2003).
[CrossRef]

Jolesz, F. A.

G. Gerig, O. Kubler, R. Kikinis, and F. A. Jolesz, "Nonlinear anisotropic filtering of mri data," IEEE Trans. Med. Imaging 11, 221-232 (1992).
[CrossRef] [PubMed]

Kikinis, R.

G. Gerig, O. Kubler, R. Kikinis, and F. A. Jolesz, "Nonlinear anisotropic filtering of mri data," IEEE Trans. Med. Imaging 11, 221-232 (1992).
[CrossRef] [PubMed]

Kim, E.

J. Kim, D. T. Miller, E. Kim, S. Oh, J. Oh, and T. E. Milner, "Optical coherence tomography speckle reduction by a partially spatially coherent source," J. Biomed. Opt. 10, 64034 -9 (2005).
[CrossRef]

Kim, J.

J. Kim, D. T. Miller, E. Kim, S. Oh, J. Oh, and T. E. Milner, "Optical coherence tomography speckle reduction by a partially spatially coherent source," J. Biomed. Opt. 10, 64034 -9 (2005).
[CrossRef]

Ko, T. H.

Koenderink, J.

J. Koenderink, "The structure of images," Biol. Cybern. 50, 363-370 (1984).
[CrossRef] [PubMed]

Kubler, O.

G. Gerig, O. Kubler, R. Kikinis, and F. A. Jolesz, "Nonlinear anisotropic filtering of mri data," IEEE Trans. Med. Imaging 11, 221-232 (1992).
[CrossRef] [PubMed]

Leitgeb, R.

M. Pircher, E. Götzinger, R. Leitgeb, A.F. Fercher, and C. K. Hitzenberger, "Speckle reduction in optical coherence tomography by frequency compounding," J. Biomed. Opt. 8, 565-569 (2003).
[CrossRef] [PubMed]

Lions, P. L.

F. Catte, P. L. Lions, J. M. Morel, and T. Coll, "Image selective smoothing and edge detection by nonlinear diffusion," SIAM J. Numer. Anal. 29, 182-193 (1992).
[CrossRef]

Malchow, D.

Malik, J.

P. Perona and J. Malik, "Scale-space and edge detection using anisotropic diffusion," IEEE Trans. Pattern Anal. and Mach. Intell. 12, 629-639 (1990).
[CrossRef]

Miller, D. T.

J. Kim, D. T. Miller, E. Kim, S. Oh, J. Oh, and T. E. Milner, "Optical coherence tomography speckle reduction by a partially spatially coherent source," J. Biomed. Opt. 10, 64034 -9 (2005).
[CrossRef]

Milner, T. E.

J. Kim, D. T. Miller, E. Kim, S. Oh, J. Oh, and T. E. Milner, "Optical coherence tomography speckle reduction by a partially spatially coherent source," J. Biomed. Opt. 10, 64034 -9 (2005).
[CrossRef]

Morel, J. M.

F. Catte, P. L. Lions, J. M. Morel, and T. Coll, "Image selective smoothing and edge detection by nonlinear diffusion," SIAM J. Numer. Anal. 29, 182-193 (1992).
[CrossRef]

Motaghiannezam, S. M. R.

Noble, A.

G. Sanchez-Ortiz and A. Noble, "Fuzzy clustering driven anisotropic diffusion: Enhancement and segmentation of cardiac MR images," in IEEE Nuclear Symp. and Med. Imag. Conf.  3, 1873-1874 (1998).

Oh, J.

J. Kim, D. T. Miller, E. Kim, S. Oh, J. Oh, and T. E. Milner, "Optical coherence tomography speckle reduction by a partially spatially coherent source," J. Biomed. Opt. 10, 64034 -9 (2005).
[CrossRef]

Oh, S.

J. Kim, D. T. Miller, E. Kim, S. Oh, J. Oh, and T. E. Milner, "Optical coherence tomography speckle reduction by a partially spatially coherent source," J. Biomed. Opt. 10, 64034 -9 (2005).
[CrossRef]

Oh, W. Y.

Ozcan, A.

A. Ozcan, A. Bilenca, A. E. Desjardins, B. E. Bouma, and G. J. Tearney, "Speckle reduction in optical coherence tomography images using digital filtering," J. Opt. Soc. Am. A. 24, 1901-1910 (2007).
[CrossRef]

Perona, P.

P. Perona and J. Malik, "Scale-space and edge detection using anisotropic diffusion," IEEE Trans. Pattern Anal. and Mach. Intell. 12, 629-639 (1990).
[CrossRef]

Pircher, M.

M. Pircher, E. Götzinger, R. Leitgeb, A.F. Fercher, and C. K. Hitzenberger, "Speckle reduction in optical coherence tomography by frequency compounding," J. Biomed. Opt. 8, 565-569 (2003).
[CrossRef] [PubMed]

Puliafito, C. A.

Puvanathasan, P.

Ren, Z.

Rogowska, J.

J. Rogowska and M. E. Brezinski, "Evaluation of the adaptive speckle suppression filter for coronary optical coherence tomography imaging," IEEE Trans. Med. Imaging 19, 1261-1266 (2000).
[CrossRef]

Ruiz, J.

S. Aja, C. Alberola, and J. Ruiz, "Fuzzy anisotropic diffusion for speckle filtering," in IEEE Int. Conf. Acoust. Speech Signal Process.  2, 1261-1264 (2001).

Salinas, H. M.

H. M. Salinas and D. C. Fernandez, "Comparison of pde-based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography," IEEE Trans. Med. Imaging 26, 761-771 (2007).
[CrossRef] [PubMed]

D. C. Fernandez, H. M. Salinas and C. A. Puliafito, "Automated detection of retinal layer structures on optical coherence tomography images," Opt. Express 13, 10200-10216 (2005).
[CrossRef]

D. C. Fernandez and H. M. Salinas, "Evaluation of a nonlinear diffusion process for segmentation and quantification of lesions in optical coherence tomography images," Proc. SPIE 5747, 1834-1843 (2005).
[CrossRef]

Sanchez-Ortiz, G.

G. Sanchez-Ortiz and A. Noble, "Fuzzy clustering driven anisotropic diffusion: Enhancement and segmentation of cardiac MR images," in IEEE Nuclear Symp. and Med. Imag. Conf.  3, 1873-1874 (1998).

Schmitt, J. M.

J. M. Schmitt, S. H. Xiang, and K. M. Yung, "Speckle in optical coherence tomography," J. Bio. Opt. 4, 95-105 (1999).
[CrossRef]

Tearney, G. J.

A. E. Desjardins, B. J. Vakoc, W. Y. Oh, S. M. R. Motaghiannezam, G. J. Tearney, and B. E. Bouma, "Angle-resolved Optical Coherence Tomography with sequential angular selectivity for speckle reduction," Opt. Express 15, 6200-6209 (2007).
[CrossRef] [PubMed]

A. Ozcan, A. Bilenca, A. E. Desjardins, B. E. Bouma, and G. J. Tearney, "Speckle reduction in optical coherence tomography images using digital filtering," J. Opt. Soc. Am. A. 24, 1901-1910 (2007).
[CrossRef]

N. Iftimia, B. E. Bouma, and G. J. Tearney, "Speckle reduction in optical coherence tomography by path length encoded angular compounding," J. Bio. Opt. 8, 260-263 (2003).
[CrossRef]

Vakoc, B. J.

Wang, R. K.

R. K. Wang, "Reduction of speckle noise for optical coherence tomography by the use of nonlinear anisotropic diffusion," Proc. SPIE 5690, 380-385 (2005).
[CrossRef]

Xiang, S. H.

J. M. Schmitt, S. H. Xiang, and K. M. Yung, "Speckle in optical coherence tomography," J. Bio. Opt. 4, 95-105 (1999).
[CrossRef]

Yung, K. M.

J. M. Schmitt, S. H. Xiang, and K. M. Yung, "Speckle in optical coherence tomography," J. Bio. Opt. 4, 95-105 (1999).
[CrossRef]

Zadeh, L. A.

L. A. Zadeh, "Fuzzy sets," Information Control 8, 338-353 (1965).
[CrossRef]

Biol. Cybern.

J. Koenderink, "The structure of images," Biol. Cybern. 50, 363-370 (1984).
[CrossRef] [PubMed]

IEEE Trans. Med. Imaging

H. M. Salinas and D. C. Fernandez, "Comparison of pde-based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography," IEEE Trans. Med. Imaging 26, 761-771 (2007).
[CrossRef] [PubMed]

J. Rogowska and M. E. Brezinski, "Evaluation of the adaptive speckle suppression filter for coronary optical coherence tomography imaging," IEEE Trans. Med. Imaging 19, 1261-1266 (2000).
[CrossRef]

G. Gerig, O. Kubler, R. Kikinis, and F. A. Jolesz, "Nonlinear anisotropic filtering of mri data," IEEE Trans. Med. Imaging 11, 221-232 (1992).
[CrossRef] [PubMed]

IEEE Trans. Pattern Anal. and Mach. Intell.

P. Perona and J. Malik, "Scale-space and edge detection using anisotropic diffusion," IEEE Trans. Pattern Anal. and Mach. Intell. 12, 629-639 (1990).
[CrossRef]

Information Control

L. A. Zadeh, "Fuzzy sets," Information Control 8, 338-353 (1965).
[CrossRef]

J. Bio. Opt.

W. Drexler, "Ultrahigh-resolution optical coherence tomography," J. Bio. Opt. 9, 47-74 (2004).
[CrossRef]

J. M. Schmitt, S. H. Xiang, and K. M. Yung, "Speckle in optical coherence tomography," J. Bio. Opt. 4, 95-105 (1999).
[CrossRef]

N. Iftimia, B. E. Bouma, and G. J. Tearney, "Speckle reduction in optical coherence tomography by path length encoded angular compounding," J. Bio. Opt. 8, 260-263 (2003).
[CrossRef]

J. Biomed. Opt.

J. Kim, D. T. Miller, E. Kim, S. Oh, J. Oh, and T. E. Milner, "Optical coherence tomography speckle reduction by a partially spatially coherent source," J. Biomed. Opt. 10, 64034 -9 (2005).
[CrossRef]

M. Pircher, E. Götzinger, R. Leitgeb, A.F. Fercher, and C. K. Hitzenberger, "Speckle reduction in optical coherence tomography by frequency compounding," J. Biomed. Opt. 8, 565-569 (2003).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A.

A. Ozcan, A. Bilenca, A. E. Desjardins, B. E. Bouma, and G. J. Tearney, "Speckle reduction in optical coherence tomography images using digital filtering," J. Opt. Soc. Am. A. 24, 1901-1910 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

D. C. Fernandez and H. M. Salinas, "Evaluation of a nonlinear diffusion process for segmentation and quantification of lesions in optical coherence tomography images," Proc. SPIE 5747, 1834-1843 (2005).
[CrossRef]

R. K. Wang, "Reduction of speckle noise for optical coherence tomography by the use of nonlinear anisotropic diffusion," Proc. SPIE 5690, 380-385 (2005).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Block diagram of the Fuzzy Type II Adaptive Diffusion algorithm.

Fig. 2.
Fig. 2.

Interval Type II Fuzzy Membership functions for the fuzzy variables a) “low edginess measure” and b) “high noisiness measure”.

Fig. 3.
Fig. 3.

Human finger tip image, 1000 × 512 pixels, corresponding to 1 mm × 0.8 mm, processed with the following filters: Original image (a), Wiener (b), Adaptive Lee (c), Type I Fuzzy AD (d), Type II Fuzzy Wavelet (e) and Type II Fuzzy AD (f). The red and green line boxes in (a) mark the selected regions for the image metrics evaluation. The red arrows in (b) -(f) point at sweat glands in the epidermis. The blue line box in (a) marks a region containing sweat glands, that has been enlarged 2x and shown as an inset in (a). Similar insets are shown in the processed images (b) – (f). Enlarged copies of all insets are shown in (g) – (l) for close comparison of the performance of the five speckle reduction algorithms.

Fig. 4.
Fig. 4.

An OCT image of a human retina (1000 × 512), processed with the following filters: Original image (a), Wiener (b), Adaptive Lee (c), Type I Fuzzy AD (d), Type II Fuzzy Wavelet (e) and Type II Fuzzy AD (f). The blue-line box in (a) marks a region containing a choroidal blood vessel, (red arrows). Similar regions were selected for the filtered images and enlarged copies of them are shown in (g) – (l) for close comparison of the performance of all image processing algorithms. Blue arrows mark the inner – outer segment junction in the photoreceptor layer.

Tables (2)

Tables Icon

Table 1. Image quality metrics evaluated for the human finger tip image. Values are relative to the original image.

Tables Icon

Table 2. Image quality metrics evaluated for the human retina image. Values are relative to the original image.

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

u(x,y,t)t=c(t)Δu(x,y,t)
c(x,y,t)={largeinhomogeneousimageregionssmallnearimageedges
x=[101101101]andy=[111000111]
c(x,y,t)=g(Gσ*medx*(Gσ*I)2+y*(Gσ*I)2)
g(x)=11+xK2
E(x,y,t)=Gσ*medx*(Gσ*I)2+y*(Gσ*I)2
N(x,y,t)=I(x,y,t)1(2K+1)21i=Ki=Kj=Kj=KIp(x+i,y+j,t)
γx,y,tUpper=μAUpper(E(x,y,t))·μBUpper(N(x,y,t))
γx,y,tLower=μALower(E(x,y,t))·μBLower(N(x,y,t))
c(x,y,t)=γx,y,tUpper+γx,y,tLower2
I(x,y,t)t =c(x,y,t) Δ I (x,y,t)=c(x,y,t) I (x,y,t) =[c(x,y,t)I(x,y,t)]=
=div c (x,y,t) I (x,y,t) ] =x[c(x,y,t)xI(x,y,t)]+yc(x,y,t)xI(x,y,t)]
I(x,y,t)t=1Δx2c(x+Δx2,y,t) [I(x+Δx2,y,t)I(x,y,t)] 1Δx2c(xΔx2,y,t)
[I(x,y,t)I(xΔx2,y,t)]+1Δy2c(x,y+Δy2,t)[I(x,y+Δy,t)I(x,y,t)]
1Δy2c(x,y+Δy2,t) [I(x,y,t)I(x,y+Δy,t)]
I(x,y,t+Δt)I(x,y,t)tI(x,y,t)+I(x,y,t)tΔt
SNR=10log10(max(I2)σn2)
ENL=1H(h=1Hμh2σh2)
CNR=1R(r=1R(μrμb)σr2+σb2)
η=ij(ΔIi,jΔĪi,j)·(ΔÎi,jΔÎ̄i,j)ij(ΔIi,jΔĪi,j)·(ΔIi,jΔĪi,j)·ijr(ΔÎi,jΔÎ̄i,j)·(ΔÎΔÎ̄i,j)

Metrics