Abstract

A novel speckle reduction technique based on soft thresholding of wavelet coefficients using interval type II fuzzy system was developed for reducing speckle noise in Optical Coherence Tomography images. The proposed algorithm is an extension of a recently published method for filtering additive Gaussian noise by use of type I fuzzy system. Unlike type I, interval type II fuzzy based thresholding filter considers the uncertainty in the calculated threshold and the wavelet coefficient is adjusted based on this uncertainty. A single parameter controls the signal-to-noise (SNR) improvement. Application of this novel algorithm to optical coherence tomograms acquired in-vivo from a human finger tip show reduction in the speckle noise with little edge blurring and image SNR improvement of about 10dB. Comparison with adaptive Wiener and adaptive Lee filters, applied to the same image, demonstrated the superior performance of the fuzzy type II algorithm in terms of image metrics improvement.

© 2007 Optical Society of America

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  1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
    [CrossRef] [PubMed]
  2. W. Drexler, "Ultrahigh-resolution optical coherence tomography," J. Bio. Opt. 9, 47-74 (2004).
    [CrossRef]
  3. J. M. Schmitt, S. H. Xiang, and K. M. Yung, "Speckle in optical coherence tomography," J. Bio. Opt. 4, 95-105 (1999).
    [CrossRef]
  4. J. Rogowska and M. E. Brezinski, "Evaluation of the adaptive speckle suppression filter for coronary optical coherence tomography imaging," IEEE Trans. Med. Imaging,  19, 1261-6 (2000).
    [CrossRef]
  5. D. C. Adler, T. H. Ko, and J. G. Fujimoto, "Speckle reduction in optical coherence tomography images by use of a spatially adaptive wavelet filter," Opt. Lett. 29, 2878-2880 (2004).
    [CrossRef]
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    [CrossRef]
  7. Y. H. Lu, S. Y. Tan, T. S. Yeo, W. E. Ng, I. Lim, and C. B. Zhang, "Adaptive filtering algorithms for SAR speckle reduction, " Proc. IGARSS 1, 67-69 (1996).
  8. 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 -64039 (2005).
    [CrossRef]
  9. T. M. Jorgensen, L. Thrane, M. Mogensen, F. Pedersen and P. E. Andersen, "Speckle reduction in optical coherence tomography images of human skin by a spatial diversity method," Proc. SPIE. 6627, 66270P (2007).
    [CrossRef]
  10. 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]
  11. 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]
  12. S. Schulte, B. Huysmans, A. Pizurica, E. E. Kerre, and W. Philips, "A new fuzzy-based wavelet shrinkage image denoising technique," Lecture Notes in Computer Science,  4179, 12-23 (2006).
    [CrossRef]
  13. H. L. Resnikoff and R. O. WellsJr, "Wavelet Analysis: The Scalable Structure of Information," R. K. Wang, "Reduction of speckle noise for optical coherence tomography by the use of nonlinear anisotropic diffusion," Proc. SPIE. 5690, 380-385 (2005).
  14. L. A. Zadeh, "Fuzzy sets," Information Control,  8, 338-353 (1965).
    [CrossRef]
  15. P. Baroni, G. Guida, and S. Mussi, "Enhancing Cognitive Plausibility of Uncertainty Calculus: A Common-Sense-Based Approach to Propagation and Aggregation," IEEE Trans. Systems, Man, and Cybernetics,  28, 394-407 (1998).
    [CrossRef]
  16. Y. Li and C. Moloney, "Selective Wavelet Coefficient Soft-Thresholding Scheme for Speckle Noise Reduction in SAR Images," IEEE Workshop on Nonlinear Signal and Image Processing, (1997).
  17. H. R. Tizhoosh, "Image Thresholding using type II fuzzy sets," Pattern Recognition,  38, 2363-2372 (2005).
    [CrossRef]
  18. S. Gupta et al., "A wavelet based statistical approach for speckle reduction in medical ultrasound images," in Proc.IEEE TENCON,  2, 534-537 (2003).
  19. S. Gupta, L. Kaur, R. C. Chauhan, and S. C. Saxena, "A wavelet based statistical approach for speckle reduction in medical ultrasound images," in Proc.IEEE TENCON,  2, 534-537 (2003).
  20. F. Sattar, L. Floreby, G. Salomonsson, and B. Lovstrom, "Image enhancement based on a nonlinear multiscale method," IEEE Trans. Image Process. 6, 888-895 (1997).
    [CrossRef] [PubMed]
  21. D. Gnanadurai and V. Sadasivam, "Undecimated wavelet based speckle reduction for SAR images," Pattern Recognition Letters,  26, 793-800 (2005).
    [CrossRef]
  22. R. C. Gonzalez and R. E. Woods, Digital Image Processing, Second Ed (Prentice-Hall, New Jersey, 2002).
  23. S. J. Lim, Two-Dimensional Signal and Image Processing, Prentice Hall (1990).

2007

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]

T. M. Jorgensen, L. Thrane, M. Mogensen, F. Pedersen and P. E. Andersen, "Speckle reduction in optical coherence tomography images of human skin by a spatial diversity method," Proc. SPIE. 6627, 66270P (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]

2006

S. Schulte, B. Huysmans, A. Pizurica, E. E. Kerre, and W. Philips, "A new fuzzy-based wavelet shrinkage image denoising technique," Lecture Notes in Computer Science,  4179, 12-23 (2006).
[CrossRef]

2005

H. L. Resnikoff and R. O. WellsJr, "Wavelet Analysis: The Scalable Structure of Information," R. K. Wang, "Reduction of speckle noise for optical coherence tomography by the use of nonlinear anisotropic diffusion," Proc. SPIE. 5690, 380-385 (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 -64039 (2005).
[CrossRef]

H. R. Tizhoosh, "Image Thresholding using type II fuzzy sets," Pattern Recognition,  38, 2363-2372 (2005).
[CrossRef]

D. Gnanadurai and V. Sadasivam, "Undecimated wavelet based speckle reduction for SAR images," Pattern Recognition Letters,  26, 793-800 (2005).
[CrossRef]

2004

2003

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]

S. Gupta et al., "A wavelet based statistical approach for speckle reduction in medical ultrasound images," in Proc.IEEE TENCON,  2, 534-537 (2003).

S. Gupta, L. Kaur, R. C. Chauhan, and S. C. Saxena, "A wavelet based statistical approach for speckle reduction in medical ultrasound images," in Proc.IEEE TENCON,  2, 534-537 (2003).

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, 1261-6 (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]

1998

P. Baroni, G. Guida, and S. Mussi, "Enhancing Cognitive Plausibility of Uncertainty Calculus: A Common-Sense-Based Approach to Propagation and Aggregation," IEEE Trans. Systems, Man, and Cybernetics,  28, 394-407 (1998).
[CrossRef]

1997

F. Sattar, L. Floreby, G. Salomonsson, and B. Lovstrom, "Image enhancement based on a nonlinear multiscale method," IEEE Trans. Image Process. 6, 888-895 (1997).
[CrossRef] [PubMed]

1996

Y. H. Lu, S. Y. Tan, T. S. Yeo, W. E. Ng, I. Lim, and C. B. Zhang, "Adaptive filtering algorithms for SAR speckle reduction, " Proc. IGARSS 1, 67-69 (1996).

1991

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

1965

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

IEEE TENCON

S. Gupta et al., "A wavelet based statistical approach for speckle reduction in medical ultrasound images," in Proc.IEEE TENCON,  2, 534-537 (2003).

S. Gupta, L. Kaur, R. C. Chauhan, and S. C. Saxena, "A wavelet based statistical approach for speckle reduction in medical ultrasound images," in Proc.IEEE TENCON,  2, 534-537 (2003).

IEEE Trans. Image Process.

F. Sattar, L. Floreby, G. Salomonsson, and B. Lovstrom, "Image enhancement based on a nonlinear multiscale method," IEEE Trans. Image Process. 6, 888-895 (1997).
[CrossRef] [PubMed]

IEEE Trans. Med. Imaging

J. Rogowska and M. E. Brezinski, "Evaluation of the adaptive speckle suppression filter for coronary optical coherence tomography imaging," IEEE Trans. Med. Imaging,  19, 1261-6 (2000).
[CrossRef]

IEEE Trans. Systems, Man, and Cybernetics

P. Baroni, G. Guida, and S. Mussi, "Enhancing Cognitive Plausibility of Uncertainty Calculus: A Common-Sense-Based Approach to Propagation and Aggregation," IEEE Trans. Systems, Man, and Cybernetics,  28, 394-407 (1998).
[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 -64039 (2005).
[CrossRef]

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]

Lecture Notes in Computer Science

S. Schulte, B. Huysmans, A. Pizurica, E. E. Kerre, and W. Philips, "A new fuzzy-based wavelet shrinkage image denoising technique," Lecture Notes in Computer Science,  4179, 12-23 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Pattern Recognition

H. R. Tizhoosh, "Image Thresholding using type II fuzzy sets," Pattern Recognition,  38, 2363-2372 (2005).
[CrossRef]

Pattern Recognition Letters

D. Gnanadurai and V. Sadasivam, "Undecimated wavelet based speckle reduction for SAR images," Pattern Recognition Letters,  26, 793-800 (2005).
[CrossRef]

Proc. IGARSS

Y. H. Lu, S. Y. Tan, T. S. Yeo, W. E. Ng, I. Lim, and C. B. Zhang, "Adaptive filtering algorithms for SAR speckle reduction, " Proc. IGARSS 1, 67-69 (1996).

Proc. SPIE.

H. L. Resnikoff and R. O. WellsJr, "Wavelet Analysis: The Scalable Structure of Information," R. K. Wang, "Reduction of speckle noise for optical coherence tomography by the use of nonlinear anisotropic diffusion," Proc. SPIE. 5690, 380-385 (2005).

T. M. Jorgensen, L. Thrane, M. Mogensen, F. Pedersen and P. E. Andersen, "Speckle reduction in optical coherence tomography images of human skin by a spatial diversity method," Proc. SPIE. 6627, 66270P (2007).
[CrossRef]

Science

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Other

Y. Li and C. Moloney, "Selective Wavelet Coefficient Soft-Thresholding Scheme for Speckle Noise Reduction in SAR Images," IEEE Workshop on Nonlinear Signal and Image Processing, (1997).

R. C. Gonzalez and R. E. Woods, Digital Image Processing, Second Ed (Prentice-Hall, New Jersey, 2002).

S. J. Lim, Two-Dimensional Signal and Image Processing, Prentice Hall (1990).

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Figures (4)

Fig. 1.
Fig. 1.

Two-dimensional wavelet decomposition at level j and j+1. The intra-scale and interscale relationship among the horizontal (H), vertical (V) and diagonal (D) detail coefficients is shown.

Fig. 2.
Fig. 2.

Interval Type II Fuzzy Membership functions for the fuzzy variables a) “large magnitude wavelet coefficient” and b) “large correlation map value”.

Fig. 3.
Fig. 3.

Wavelet denoising of a human finger tip image acquired with the FD-OCT 1060nm system: A) Original OCT image. B) Adaptive Wiener filtered image. C) Adaptive Lee filtered image and D) type II fuzzy wavelet filtered image. The images are 1000×512 (lateral × axial) pixels, corresponding to 1 mm×0.8 mm physical dimensions. The red and yellow line boxes in A) mark the selected regions for the image metrics evaluation. The red arrows in B)-D) point at sweat glands in the epidermis. The blue line box in A) marks a region containing sweat glands, that has been enlarged and shown as a 2× inset in image A). Similar insets were generated for the processed images B) - D). Enlarged copies of all four insets are shown in E) - H) for close comparison of the performance of the three wavelet algorithms. E) Original unprocessed image, F) Adaptive Wiener, G) Adaptive Lee and H) Fuzzy Type II set algorithms.

Fig. 4.
Fig. 4.

SNR improvement as a function of η. Maximum SNR is obtained at η=0.4325.

Tables (1)

Tables Icon

Table 1. Image quality metrics for human finger tip OCT image

Equations (18)

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

f ( m , n ) = s ( m , n ) n ( m , n ) + n a ( m , n )
f L ( m , n ) = s L ( m , n ) + n L ( m , n )
f j , d ( m , n ) = s j , d ( m , n ) + n j , d ( m , n )
w j , d ( m , n ) = f j , d ( m , n )
x j , d ( m , n ) = int er j , d ( m , n ) · int ra j , d ( m , n )
int er j , d ( m , n ) = a = N a = N b = N b = N f j , d ( m + a , n + b ) · f j + 1 , d ( m + a , n + b )
int ra j , d ( m , n ) = a = N a = N b = N b = N f j , d ( m + a , n + b )
μ ( x ) = 1 1 + e c x w
μ A Upper = [ μ A ( x ) ] 1 β and μ A Lower = [ μ A ( x ) ] β
μ B Upper = [ μ B ( x ) ] 1 β and μ B Lower = [ μ B ( x ) ] β
α j , d Upper ( m , n ) = μ A Upper ( w j , d ( m , n ) ) · μ B Upper ( x j , d ( m , n ) )
α j , d Lower ( m , n ) = μ A Lower ( w j , d ( m , n ) ) · μ B Lower ( x j , d ( m , n ) )
γ j , d ( m , n ) = α j , d Upper ( m , n ) + α j , d Lower ( m , n ) 2
f ̂ j , d ( m , n ) = f j , d ( m , n ) · γ j , d ( m , n )
SNR = 10 log 10 ( max ( I 2 ) σ n 2 )
ENL = 1 H ( h = 1 H μ h 2 σ h 2 )
CNR = 1 R ( r = 1 R ( μ r μ b ) σ r 2 + σ b 2 )
= 1 R ( r = 1 R ( i , j ) r ( Δ I Δ I ̅ ) · ( Δ I ̂ Δ I ̂ ̅ ) ( i , j ) r ( Δ I Δ I ̅ ) · ( Δ I Δ I ̅ ) · ( i , j ) r ( Δ I ̂ Δ I ̂ ̅ ) · ( Δ I ̂ Δ I ̂ ̅ ) )

Metrics