Abstract

In many image-processing applications the noise that corrupts the images is signal dependent, the most widely encountered types being multiplicative, Poisson, film-grain, and speckle noise. Their common feature is that the power of the noise is related to the brightness of the corrupted pixel. This results in brighter areas appearing to be noisier than darker areas. We propose a new adaptive-neighborhood approach to filtering images corrupted by signal-dependent noise. Instead of using fixed-size, fixed-shape neighborhoods, statistics of the noise and the signal are computed within variable-size, variable-shape neighborhoods that are grown for every pixel to contain only pixels that belong to the same object. Results of adaptive-neighborhood filtering are compared with those given by two local-statistics-based filters (the refined Lee filter and the noise-updating repeated Wiener filter), both in terms of subjective and objective measures. The adaptive-neighborhood approach provides better noise suppression as indicated by lower mean-squared errors as well as better retention of edge sharpness than the other approaches considered.

© 1998 Optical Society of America

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References

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  1. J. S. Lee, “Refined filtering of image noise using local statistics,” Comput. Graphics Image Process. 15, 380–389 (1981).
    [CrossRef]
  2. J. S. Lee, “Speckle analysis and smoothing of synthetic aperture radar images,” Comput. Graphics Image Process. 17, 24–32 (1981).
    [CrossRef]
  3. J. S. Lee, “Digital image enhancement and noise filtering by use of local statistics,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-2, 165–168 (1980).
    [CrossRef]
  4. D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, “Adaptive noise smoothing filter for images with signal-dependent noise,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-7, 165–177 (1985).
    [CrossRef]
  5. D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, “Adaptive restoration of images with speckle,” IEEE Trans. Acoust. Speech Signal Process. 35, 373–383 (1987).
    [CrossRef]
  6. F. Naderi, A. A. Sawchuk, “Estimation of images degraded by film-grain noise,” Appl. Opt. 17, 1228–1237 (1978).
    [CrossRef] [PubMed]
  7. G. K. Froehlich, J. F. Walkup, T. F. Krile, “Estimation in signal-dependent film-grain noise,” Appl. Opt. 20, 3619–3626 (1981).
    [CrossRef] [PubMed]
  8. C. M. Lo, A. A. Sawchuk, “Nonlinear restoration of filtered images with Poisson noise,” in Applied Digital Image Processing III, A. G. Tescher, ed., Proc. SPIE207, 84–95 (1979).
    [CrossRef]
  9. S. S. Jiang, A. A. Sawchuk, “Noise updating repeated Wiener filter and other adaptive noise smoothing filters using local image statistics,” Appl. Opt. 25, 2326–2337 (1986).
    [CrossRef] [PubMed]
  10. M. A. Schultze, “An edge-enhancing nonlinear filter for reducing multiplicative noise,” in Nonlinear Image Processing VIII, E. R. Dougherty, J. T. Astola, eds., Proc. SPIE3026, 46–56 (1997).
    [CrossRef]
  11. J. D. Downie, J. F. Walkup, “Optimal correlation filters with signal-dependent noise,” J. Opt. Soc. Am. A 11, 1599–1609 (1994).
    [CrossRef]
  12. K. E. Barner, G. R. Arce, “Optimal detection methods for the restoration of images degraded by signal-dependent noise,” in Visual Communications and Image Processing IV, W. A. Pearlman, ed., Proc. SPIE1199, 115–124 (1989).
    [CrossRef]
  13. R. Kasturi, J. F. Walkup, T. F. Krile, “Image restoration by transformation of signal-dependent noise to signal-independent noise,” Appl. Opt. 22, 3537–3542 (1983).
    [CrossRef] [PubMed]
  14. H. H. Arsenault, C. Gendron, M. Denis, “Transformation of film-grain noise into signal-independent Gaussian noise,” J. Opt. Soc. Am. 71, 91–94 (1981).
    [CrossRef]
  15. H. H. Arsenault, M. Levesque, “Combined homomorphic and local-statistics processing for restoration of images degraded by signal-dependent noise,” Appl. Opt. 23, 845–850 (1984).
    [CrossRef] [PubMed]
  16. R. B. Paranjape, R. M. Rangayyan, W. M. Morrow, “Adaptive neighborhood mean and median filtering,” J. Electron. Imag. 3, 360–367 (1994).
    [CrossRef]
  17. R. B. Paranjape, T. F. Rabie, R. M. Rangayyan, “Image restoration by adaptive neighborhood noise subtraction,” Appl. Opt. 33, 1861–1869 (1994).
    [CrossRef]
  18. A. Das, R. M. Rangayyan, “Adaptive region-based filtering of multiplicative noise,” in Nonlinear Image Processing VIII, E. R. Dougherty, J. T. Astola, eds., Proc. SPIE3026, 338–348 (1997).
    [CrossRef]
  19. R. M. Rangayyan, A. Das, “Filtering multiplicative noise in images using adaptive region-based statistics,” J. Electron. Imag. 7, 222–230 (1998).
    [CrossRef]
  20. N. D. A. Mascarenhas, “An overview of speckle noise filtering in SAR images,” in T. D. Guyenne, editor, Proc. First Latin American Seminar on Radar Remote Sensing: Image Processing Techniques (European Space Agency, 1996), Vol. 1, pp. 71–79.
  21. J. S. Lim, H. Nawab, “Techniques for speckle noise removal,” Opt. Eng. 21, 472–480 (1981).
  22. I. Pitas, A. N. Venetsanopoulos, “Order statistics in digital image processing,” Proc. IEEE 80, 1893–1923 (1992).
    [CrossRef]

1998 (1)

R. M. Rangayyan, A. Das, “Filtering multiplicative noise in images using adaptive region-based statistics,” J. Electron. Imag. 7, 222–230 (1998).
[CrossRef]

1994 (3)

R. B. Paranjape, R. M. Rangayyan, W. M. Morrow, “Adaptive neighborhood mean and median filtering,” J. Electron. Imag. 3, 360–367 (1994).
[CrossRef]

R. B. Paranjape, T. F. Rabie, R. M. Rangayyan, “Image restoration by adaptive neighborhood noise subtraction,” Appl. Opt. 33, 1861–1869 (1994).
[CrossRef]

J. D. Downie, J. F. Walkup, “Optimal correlation filters with signal-dependent noise,” J. Opt. Soc. Am. A 11, 1599–1609 (1994).
[CrossRef]

1992 (1)

I. Pitas, A. N. Venetsanopoulos, “Order statistics in digital image processing,” Proc. IEEE 80, 1893–1923 (1992).
[CrossRef]

1987 (1)

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, “Adaptive restoration of images with speckle,” IEEE Trans. Acoust. Speech Signal Process. 35, 373–383 (1987).
[CrossRef]

1986 (1)

1985 (1)

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, “Adaptive noise smoothing filter for images with signal-dependent noise,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-7, 165–177 (1985).
[CrossRef]

1984 (1)

1983 (1)

1981 (5)

H. H. Arsenault, C. Gendron, M. Denis, “Transformation of film-grain noise into signal-independent Gaussian noise,” J. Opt. Soc. Am. 71, 91–94 (1981).
[CrossRef]

G. K. Froehlich, J. F. Walkup, T. F. Krile, “Estimation in signal-dependent film-grain noise,” Appl. Opt. 20, 3619–3626 (1981).
[CrossRef] [PubMed]

J. S. Lee, “Refined filtering of image noise using local statistics,” Comput. Graphics Image Process. 15, 380–389 (1981).
[CrossRef]

J. S. Lee, “Speckle analysis and smoothing of synthetic aperture radar images,” Comput. Graphics Image Process. 17, 24–32 (1981).
[CrossRef]

J. S. Lim, H. Nawab, “Techniques for speckle noise removal,” Opt. Eng. 21, 472–480 (1981).

1980 (1)

J. S. Lee, “Digital image enhancement and noise filtering by use of local statistics,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-2, 165–168 (1980).
[CrossRef]

1978 (1)

Arce, G. R.

K. E. Barner, G. R. Arce, “Optimal detection methods for the restoration of images degraded by signal-dependent noise,” in Visual Communications and Image Processing IV, W. A. Pearlman, ed., Proc. SPIE1199, 115–124 (1989).
[CrossRef]

Arsenault, H. H.

Barner, K. E.

K. E. Barner, G. R. Arce, “Optimal detection methods for the restoration of images degraded by signal-dependent noise,” in Visual Communications and Image Processing IV, W. A. Pearlman, ed., Proc. SPIE1199, 115–124 (1989).
[CrossRef]

Chavel, P.

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, “Adaptive restoration of images with speckle,” IEEE Trans. Acoust. Speech Signal Process. 35, 373–383 (1987).
[CrossRef]

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, “Adaptive noise smoothing filter for images with signal-dependent noise,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-7, 165–177 (1985).
[CrossRef]

Das, A.

R. M. Rangayyan, A. Das, “Filtering multiplicative noise in images using adaptive region-based statistics,” J. Electron. Imag. 7, 222–230 (1998).
[CrossRef]

A. Das, R. M. Rangayyan, “Adaptive region-based filtering of multiplicative noise,” in Nonlinear Image Processing VIII, E. R. Dougherty, J. T. Astola, eds., Proc. SPIE3026, 338–348 (1997).
[CrossRef]

Denis, M.

Downie, J. D.

Froehlich, G. K.

Gendron, C.

Jiang, S. S.

Kasturi, R.

Krile, T. F.

Kuan, D. T.

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, “Adaptive restoration of images with speckle,” IEEE Trans. Acoust. Speech Signal Process. 35, 373–383 (1987).
[CrossRef]

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, “Adaptive noise smoothing filter for images with signal-dependent noise,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-7, 165–177 (1985).
[CrossRef]

Lee, J. S.

J. S. Lee, “Speckle analysis and smoothing of synthetic aperture radar images,” Comput. Graphics Image Process. 17, 24–32 (1981).
[CrossRef]

J. S. Lee, “Refined filtering of image noise using local statistics,” Comput. Graphics Image Process. 15, 380–389 (1981).
[CrossRef]

J. S. Lee, “Digital image enhancement and noise filtering by use of local statistics,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-2, 165–168 (1980).
[CrossRef]

Levesque, M.

Lim, J. S.

J. S. Lim, H. Nawab, “Techniques for speckle noise removal,” Opt. Eng. 21, 472–480 (1981).

Lo, C. M.

C. M. Lo, A. A. Sawchuk, “Nonlinear restoration of filtered images with Poisson noise,” in Applied Digital Image Processing III, A. G. Tescher, ed., Proc. SPIE207, 84–95 (1979).
[CrossRef]

Mascarenhas, N. D. A.

N. D. A. Mascarenhas, “An overview of speckle noise filtering in SAR images,” in T. D. Guyenne, editor, Proc. First Latin American Seminar on Radar Remote Sensing: Image Processing Techniques (European Space Agency, 1996), Vol. 1, pp. 71–79.

Morrow, W. M.

R. B. Paranjape, R. M. Rangayyan, W. M. Morrow, “Adaptive neighborhood mean and median filtering,” J. Electron. Imag. 3, 360–367 (1994).
[CrossRef]

Naderi, F.

Nawab, H.

J. S. Lim, H. Nawab, “Techniques for speckle noise removal,” Opt. Eng. 21, 472–480 (1981).

Paranjape, R. B.

R. B. Paranjape, T. F. Rabie, R. M. Rangayyan, “Image restoration by adaptive neighborhood noise subtraction,” Appl. Opt. 33, 1861–1869 (1994).
[CrossRef]

R. B. Paranjape, R. M. Rangayyan, W. M. Morrow, “Adaptive neighborhood mean and median filtering,” J. Electron. Imag. 3, 360–367 (1994).
[CrossRef]

Pitas, I.

I. Pitas, A. N. Venetsanopoulos, “Order statistics in digital image processing,” Proc. IEEE 80, 1893–1923 (1992).
[CrossRef]

Rabie, T. F.

R. B. Paranjape, T. F. Rabie, R. M. Rangayyan, “Image restoration by adaptive neighborhood noise subtraction,” Appl. Opt. 33, 1861–1869 (1994).
[CrossRef]

Rangayyan, R. M.

R. M. Rangayyan, A. Das, “Filtering multiplicative noise in images using adaptive region-based statistics,” J. Electron. Imag. 7, 222–230 (1998).
[CrossRef]

R. B. Paranjape, T. F. Rabie, R. M. Rangayyan, “Image restoration by adaptive neighborhood noise subtraction,” Appl. Opt. 33, 1861–1869 (1994).
[CrossRef]

R. B. Paranjape, R. M. Rangayyan, W. M. Morrow, “Adaptive neighborhood mean and median filtering,” J. Electron. Imag. 3, 360–367 (1994).
[CrossRef]

A. Das, R. M. Rangayyan, “Adaptive region-based filtering of multiplicative noise,” in Nonlinear Image Processing VIII, E. R. Dougherty, J. T. Astola, eds., Proc. SPIE3026, 338–348 (1997).
[CrossRef]

Sawchuk, A. A.

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, “Adaptive restoration of images with speckle,” IEEE Trans. Acoust. Speech Signal Process. 35, 373–383 (1987).
[CrossRef]

S. S. Jiang, A. A. Sawchuk, “Noise updating repeated Wiener filter and other adaptive noise smoothing filters using local image statistics,” Appl. Opt. 25, 2326–2337 (1986).
[CrossRef] [PubMed]

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, “Adaptive noise smoothing filter for images with signal-dependent noise,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-7, 165–177 (1985).
[CrossRef]

F. Naderi, A. A. Sawchuk, “Estimation of images degraded by film-grain noise,” Appl. Opt. 17, 1228–1237 (1978).
[CrossRef] [PubMed]

C. M. Lo, A. A. Sawchuk, “Nonlinear restoration of filtered images with Poisson noise,” in Applied Digital Image Processing III, A. G. Tescher, ed., Proc. SPIE207, 84–95 (1979).
[CrossRef]

Schultze, M. A.

M. A. Schultze, “An edge-enhancing nonlinear filter for reducing multiplicative noise,” in Nonlinear Image Processing VIII, E. R. Dougherty, J. T. Astola, eds., Proc. SPIE3026, 46–56 (1997).
[CrossRef]

Strand, T. C.

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, “Adaptive restoration of images with speckle,” IEEE Trans. Acoust. Speech Signal Process. 35, 373–383 (1987).
[CrossRef]

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, “Adaptive noise smoothing filter for images with signal-dependent noise,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-7, 165–177 (1985).
[CrossRef]

Venetsanopoulos, A. N.

I. Pitas, A. N. Venetsanopoulos, “Order statistics in digital image processing,” Proc. IEEE 80, 1893–1923 (1992).
[CrossRef]

Walkup, J. F.

Appl. Opt. (6)

Comput. Graphics Image Process. (2)

J. S. Lee, “Refined filtering of image noise using local statistics,” Comput. Graphics Image Process. 15, 380–389 (1981).
[CrossRef]

J. S. Lee, “Speckle analysis and smoothing of synthetic aperture radar images,” Comput. Graphics Image Process. 17, 24–32 (1981).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process. (1)

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, “Adaptive restoration of images with speckle,” IEEE Trans. Acoust. Speech Signal Process. 35, 373–383 (1987).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (2)

J. S. Lee, “Digital image enhancement and noise filtering by use of local statistics,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-2, 165–168 (1980).
[CrossRef]

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, “Adaptive noise smoothing filter for images with signal-dependent noise,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-7, 165–177 (1985).
[CrossRef]

J. Electron. Imag. (2)

R. M. Rangayyan, A. Das, “Filtering multiplicative noise in images using adaptive region-based statistics,” J. Electron. Imag. 7, 222–230 (1998).
[CrossRef]

R. B. Paranjape, R. M. Rangayyan, W. M. Morrow, “Adaptive neighborhood mean and median filtering,” J. Electron. Imag. 3, 360–367 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

J. S. Lim, H. Nawab, “Techniques for speckle noise removal,” Opt. Eng. 21, 472–480 (1981).

Proc. IEEE (1)

I. Pitas, A. N. Venetsanopoulos, “Order statistics in digital image processing,” Proc. IEEE 80, 1893–1923 (1992).
[CrossRef]

Other (5)

K. E. Barner, G. R. Arce, “Optimal detection methods for the restoration of images degraded by signal-dependent noise,” in Visual Communications and Image Processing IV, W. A. Pearlman, ed., Proc. SPIE1199, 115–124 (1989).
[CrossRef]

N. D. A. Mascarenhas, “An overview of speckle noise filtering in SAR images,” in T. D. Guyenne, editor, Proc. First Latin American Seminar on Radar Remote Sensing: Image Processing Techniques (European Space Agency, 1996), Vol. 1, pp. 71–79.

C. M. Lo, A. A. Sawchuk, “Nonlinear restoration of filtered images with Poisson noise,” in Applied Digital Image Processing III, A. G. Tescher, ed., Proc. SPIE207, 84–95 (1979).
[CrossRef]

M. A. Schultze, “An edge-enhancing nonlinear filter for reducing multiplicative noise,” in Nonlinear Image Processing VIII, E. R. Dougherty, J. T. Astola, eds., Proc. SPIE3026, 46–56 (1997).
[CrossRef]

A. Das, R. M. Rangayyan, “Adaptive region-based filtering of multiplicative noise,” in Nonlinear Image Processing VIII, E. R. Dougherty, J. T. Astola, eds., Proc. SPIE3026, 338–348 (1997).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Flowchart of the region-growing process.

Fig. 2
Fig. 2

Region-growing steps: (a) A 25 × 25 pixel wide portion of the original Lena image. (b) Image corrupted by Poisson noise with λ = 0.1. (c) Seed pixel. (d) First step of the region-growing process on the corrupted image. The foreground pixels are in white; the background pixels are in light gray. The foreground size is limited to 100 pixels. (e) The region after inclusion of the interior background pixels. (f) The filtered image. In (c), (d) and (e) the region is superimposed over the uncorrupted image for convenience of display.

Fig. 3
Fig. 3

Results of Poisson noise filtering: (a) The original 256 × 256 pixel peppers image. (b) The image corrupted by simulated Poisson noise with λ = 0.1. (c) The image filtered with the NURW filter. (d) The image filtered with the refined Lee filter. (e) The image filtered with the ANF.

Fig. 4
Fig. 4

Results of film-grain noise filtering: (a) The original 256 × 256 pixel image. (b) The original image corrupted by film-grain noise with K = 3.3, σ1= 1, and σ2 = 0. (c) The image filtered with the NURW filter. (d) The image filtered with the refined Lee filter. (e) The image filtered with the ANF.

Fig. 5
Fig. 5

Results of speckle-noise filtering: (a) The original 256 × 256 pixel aerial image. (b) The image corrupted by speckle noise simulated as multiplicative noise with an exponential distribution averaged over four frames. (c) The image filtered with the NURW filter. (d) The image filtered with the refined Lee filter. (e) The image filtered with the ANF.

Tables (3)

Tables Icon

Table 1 MSE Values for the Noisy Images Corrupted by Simulated Poisson Noise with λ = 0.1 and the Results of Filtering

Tables Icon

Table 2 MSE Values for the Noisy Images Corrupted by Simulated Film-Grain Noise, with K = 3.3, σ1 = 1, and σ2 = 0, and the Results of Filtering

Tables Icon

Table 3 MSE Values for the Four-Frame Average Noisy Images Corrupted by Simulated Speckle Noise and the Results of Filtering

Equations (20)

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

P ġ i ,   j / f i ,   j ,   λ = λ f i ,   j ġ i , j exp - λ f i ,   j ġ i ,   j ! ,
E ġ i ,   j = λ E f i ,   j ,
g i ,   j = ġ i ,   j λ .
g i ,   j = f i ,   j + n i ,   j .
σ n 2 i ,   j = E f i ,   j λ = E g i ,   j λ .
g i ,   j = f i ,   j + K   f i ,   j   u 1 i ,   j + u 2 i ,   j ,
g i ,   j = f i ,   j + n i ,   j ,
σ n 2 i ,   j = K 2 E g i ,   j σ 1 2 + σ 2 2 .
g i ,   j = f i ,   j u i ,   j ,
g i ,   j = f i ,   j + n i ,   j ,
σ n 2 i ,   j = σ u 2 1 + σ u 2 v g i ,   j + m g 2 i ,   j ,
g = f + n ,
f ˆ = E f + C fg C g - 1 g - E g ,
f ˆ i ,   j = m g i , j + v g i ,   j - σ n 2 i ,   j v g i ,   j g i ,   j - m g i ,   j ,
σ n 1 2 i ,   j = 1 - σ n 2 i ,   j v g i ,   j + 1 2 M + 1 2 N + 1 σ n 2 i ,   j v g i ,   j 2 σ n 2 i ,   j + 1 2 M + 1 2 N + 1 σ n 2 i ,   j v g i ,   j 2 × k = i M i + M l = j N j + N ( k , l ) ( 0 , 0 )   σ n 2 k ,   l .
d kl = | g k ,   l - g i ,   j | .
T = σ n i ,   j .
MSE = 1 MN i = 0 M - 1 j = 0 N - 1 f i ,   j - f ˆ i ,   j 2 ,
σ n i ,   j v g i ,   j γ .
p u i , j x = exp - u i ,   j .

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