## Speckle noise reduction algorithm for optical coherence tomography based on interval type II fuzzy set

Optics Express, Vol. 15, Issue 24, pp. 15747-15758 (2007)

http://dx.doi.org/10.1364/OE.15.015747

Acrobat PDF (502 KB)

### 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

## 1. Introduction

*in vivo*, non-invasive, high-resolution imaging of biological tissue at superficial depths of 1–2 mm [1

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]

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]

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]

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]

6. 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]

6. 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]

6. 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]

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]

**24**, 1901–1910 (2007). [CrossRef]

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]

## 2. Theory

*W*, and

_{φ}(j,m,n), W^{H}_{ψ}(j,m,n), W^{V}_{ψ}(j,m,n)*W*respectively. The variable

^{D}ψ(j,m,n)*j*represents the decomposition scale level and(

*m,n*) represents the image spatial location. The crucial image information is compressed and represented along several resolution scales by few of these large valued coefficients [13]. Thus, by analyzing images at various resolutions, one can remove the unwanted noise, represented by the low valued coefficients.

*(W*, and

^{H}_{ψ}, W^{V}_{ψ}*W*) by soft thresholding iii) finally, reconstructing the enhanced image using inverse 2D-DWT. For an image, Mallat’s 2D-DWT can be implemented using 4 frequency channel filter banks corresponding to the four orientations. The wavelet transform of natural images has special properties like interscale and intrascale dependencies and as a result de-noising using wavelet transform has proven to be very effective. Interscale dependency refers to large wavelet coefficients propagating across the scales and intrascale dependency refers to neighbourhood of similar valued coefficients (large or small) at each scale.

^{D}ψ*s(m,n)*represents the noise free OCT image,

*f(m,n)*is the noise observation of

*s(m,n), n(m,n)*and

*n*are multiplicative speckle and additive noise respectively, and(

_{a}(m,n)*m,n*) is the variable of spatial locations. In Eq. (1), the additive noise component comes from the shot noise, light intensity noise, and electronic noise inherent in OCT imaging system and it can be ignored because it is significantly small compared to the multiplicative speckle noise [14

14. L. A. Zadeh, “Fuzzy sets,” Information Control , **8**, 338–353 (1965). [CrossRef]

*f*denotes the noisy wavelet coefficient of the observed image at scale

_{j,d}*j*and at orientation

*d, s*is the noise-free wavelet coefficient of the image and

_{j,d}*n*represents the wavelet coefficient of the speckle. Additive noise in the image domain remains additive in the transformed wavelet domain due to the linearity of the wavelet transform. The next step in the wavelet based de-noising algorithm is thresholding the detail wavelet coefficients,

_{j,d}(m,n)*f*where

_{j,d}(m,n)*d*∊{

*H,V,D*}, by use of a soft threshold. In soft thresholding if the magnitudes of the coefficients are below the threshold then they are set to zero while the coefficients with the magnitudes above the threshold are scaled towards zero. This is because the coefficients that contain mostly noise should be reduced to negligible values, while the ones containing a substantial noise free component should be reduced less. In wavelet domain different types of noise are associated with small magnitude coefficients. Important image structures are contained within the magnitude of the high coefficients. The coefficients around the threshold contain both noise and image features of interest. Therefore, an optimal threshold is reached when most of the coefficients bellow it are noise and the coefficients above it represents image features of interest.

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]

*m,n*), if the wavelet coefficient has a magnitude that is large, then the coefficient at (

*m,n*) represents image feature of interest for “almost certain” and should not be set to zero but scaled towards zero. The reason for this statement is due to the property of image edges appearing as large magnitude wavelet coefficients due to the rapid changes in intensity values. Large image structures can be found in many scales of the wavelet decomposition, but small image details can only be revealed in several fine scales and to determine small image details, interscale correlation involving two adjacent scales can be used [17

17. H. R. Tizhoosh, “Image Thresholding using type II fuzzy sets,” Pattern Recognition , **38**, 2363–2372 (2005). [CrossRef]

17. H. R. Tizhoosh, “Image Thresholding using type II fuzzy sets,” Pattern Recognition , **38**, 2363–2372 (2005). [CrossRef]

*m,n*), if the correlation map value is large, then the coefficient at (

*m,n*)represents fine image structures of interest for “almost certain” and should not be set to zero but scaled towards zero. Conversely, a correlation value close to zero indicates an area which needs to be smoothed due to noise.

*m,n*) and large correlation map value at position (

*m,n*), two fuzzy variables can be defined as follows: Large magnitude wavelet coefficient:

17. H. R. Tizhoosh, “Image Thresholding using type II fuzzy sets,” Pattern Recognition , **38**, 2363–2372 (2005). [CrossRef]

**38**, 2363–2372 (2005). [CrossRef]

*d*∊{

*H,V,D*}. The correlation map value

*x*at decomposition level

_{j,d}(m,n)*j*and orientation

*d*is based on nine wavelet coefficients in a 3×3 window (

*N*=1) at level

*j*and orientation

*d*, and the nine coefficients in the next level

*j*+1 and orientation

*d*. The subbands in each of the wavelet levels have the same size due to the Stationary Wavelet Transform (SWT) used in this manuscript. As a result the coefficients have one-to-one correspondence in terms of the position(

*m,n*).

*c*) and its width (

*w*).

*β*should be between 1 and 2 and β≫2 is usually not meaningful for image data. In this manuscript,

*β*was set to a value of 1.2. The soft threshold obtained by applying the technique in Ref. [19] was used as the center

*c*of

*µA(x)*. This is because fuzzy set A corresponds to large wavelet coefficients and the soft thresholding procedure described in Ref. [19] utilizes this information to suppress the noise. The threshold is obtained by computing the ratio of the noise variance and the standard deviation of each of the subbands. In this manuscript, the noise variance was estimated using the background region in the vertical orientation of the first subband, in a similar way as described in Ref. [5

**29**, 2878–2880 (2004). [CrossRef]

*µ*changes. The width w of

_{A}(x)*µ*and

_{A}(x)*µ*was set to a value of 0.3 after optimizing for SNR improvement while using the same center for

_{B}(x)*µ*and

_{A}(x)*µ*. Finally, the location of the MF of

_{B}(x)*µ*is controlled by a parameter η, which is the center,

_{B}(x)*c*of

*µ*. By adjusting

_{B}(x)*η*the amount of speckle removed can be varied. Thus, allowing for more or less smoothing depending on the input image being used and the amount of speckle present.

*m,n*) is “large” AND the correlation map value at (

*m,n*) is “large” then “scale towards zero the wavelet coefficient at(

*m,n*).”

*m,n*) is obtained by type reducing and defuzzifying the output from step 4. There is more than one approach to defuzzifying the output distribution; here the average of the upper and lower value is utilized.

*m,n*) which has been reduced of noise. This is obtained by applying Eq. (10). The filtering is performed at each scale of the wavelet domain and for each of the three detail coefficients (

*d*∊{

*H,V,D*}).

**29**, 2878–2880 (2004). [CrossRef]

**24**, 1901–1910 (2007). [CrossRef]

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]

**29**, 2878–2880 (2004). [CrossRef]

**24**, 1901–1910 (2007). [CrossRef]

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]

*I*and

*σ*in SNR represents the linear magnitude image and the variance of the background noise region in the linear magnitude image respectively.

^{2}_{n}*µ*and

_{h}*σ*in ENL represents the mean and variance of the

^{2}_{h}*h*homogenous region of interests respectively.

^{th}*µ*and

_{b}*σ*in CNR represents the mean and variance of the same background noise region as in SNR and

^{2}_{b}*µ*and

_{r}*σ*represents the mean and variance of the

^{2}_{r}*r*region of interest which includes the homogeneous regions as well. In the edge preservation measure, Δ

^{th}*I*and ΔÎ represent the Laplace operator performed on the original image

*I*and the filtered image Î respectively. Also, Δ

*I*̄ and ΔÎ represent the mean value in the

*r*region of interest of Δ

^{th}*I*and ΔÎ respectively.

**29**, 2878–2880 (2004). [CrossRef]

*R*=6,

*H*=3). The orthogonal Daubechies wavelet, more specifically “db4”, was utilized for the 2D-DWT with 4 levels of decomposition. The reason for using the fourth-order Daubechies wavelet is it brings smoothing effects due to the longer filter lags [21

21. D. Gnanadurai and V. Sadasivam, “Undecimated wavelet based speckle reduction for SAR images,” Pattern Recognition Letters , **26**, 793–800 (2005). [CrossRef]

**29**, 2878–2880 (2004). [CrossRef]

*conv2()*function was utilized for the convolution. Similarly, the image is reconstructed by up sampling the low scale images and convolving it with the “db4” low-pass and high-pass reconstruction filters.

*wiener2()*function. Also, a modified adaptive Lee filter implemented using an algorithm described in reference [7] was applied to the image. As mentioned before, the adaptive Wiener filter and the Lee filter were previously applied to OCT images and they showed valuable results [6

**24**, 1901–1910 (2007). [CrossRef]

## 3. Results and discussion

*in-vivo*from a human finger tip with a high speed, high resolution Fourier Domain OCT system (FD-OCT) operating in the 1060nm wavelength region. The FD-OCT system was powered with a superluminescent diode (Superlum, λc=1020nm, Δλ=108nm, P

_{out}=10mW), which provided 3. 5µm (axial) and 10µm (lateral) resolution in biological tissue. The FD-OCT system was equipped with a fast InGaAs linear array, 1024 pixel CCD camera (SUI, Goodrich) with a readout rate of 47kHz. The spectrometer was designed to fit the entire spectrum of the SLD, thus providing a maximum scanning range of 1.4mm in air. Two dimensional images (1000 A-scans×512 pixels) of a human finger tip were acquired with 1.3mW incident power and 97dB SNR at a rate of 46 frames/s.

**29**, 2878–2880 (2004). [CrossRef]

*η*to vary the amount of speckle removed by the fuzzy wavelet thresholding filter. Maximum SNR of about 10dB is achieved for

*η*=0.4325. Figure 4 shows the image SNR and a function of the parameter

*η*.

**29**, 2878–2880 (2004). [CrossRef]

*η*parameter each time the OCT system is set up. This is a somewhat time consuming task however, once optimization is achieved the algorithm can be applied to a batch of images with a very short image processing duration.

## 4. Conclusion

## Acknowledgments

## References and links

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 |

2. | W. Drexler, “Ultrahigh-resolution optical coherence tomography,” J. Bio. Opt. |

3. | J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Bio. Opt. |

4. | J. Rogowska and M. E. Brezinski, “Evaluation of the adaptive speckle suppression filter for coronary optical coherence tomography imaging,” IEEE Trans. Med. Imaging , |

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. |

6. | 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. |

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 |

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. |

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. |

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. |

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 |

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 , |

13. | H. L. Resnikoff and R. O. Wells Jr, “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 , |

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 , |

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 , |

18. | S. Gupta et al., “A wavelet based statistical approach for speckle reduction in medical ultrasound images,” in Proc. IEEE TENCON , |

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 , |

20. | F. Sattar, L. Floreby, G. Salomonsson, and B. Lovstrom, “Image enhancement based on a nonlinear multiscale method,” IEEE Trans. Image Process. |

21. | D. Gnanadurai and V. Sadasivam, “Undecimated wavelet based speckle reduction for SAR images,” Pattern Recognition Letters , |

22. | R. C. Gonzalez and R. E. Woods, |

23. | S. J. Lim, |

**OCIS Codes**

(030.6140) Coherence and statistical optics : Speckle

(100.0100) Image processing : Image processing

(100.7410) Image processing : Wavelets

(170.4500) Medical optics and biotechnology : Optical coherence tomography

(100.3008) Image processing : Image recognition, algorithms and filters

**ToC Category:**

Image Processing

**History**

Original Manuscript: October 1, 2007

Revised Manuscript: November 6, 2007

Manuscript Accepted: November 6, 2007

Published: November 12, 2007

**Virtual Issues**

Vol. 2, Iss. 12 *Virtual Journal for Biomedical Optics*

**Citation**

Prabakar Puvanathasan and Kostadinka Bizheva, "Speckle noise reduction algorithm for optical coherence tomography based on interval type II fuzzy set," Opt. Express **15**, 15747-15758 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-24-15747

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### References

- 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]
- 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]
- 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]
- 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]
- 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]
- 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).
- 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]
- 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]
- 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]
- 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]
- 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]
- 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).
- L. A. Zadeh, "Fuzzy sets," Information Control, 8, 338-353 (1965). [CrossRef]
- 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]
- 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).
- H. R. Tizhoosh, "Image Thresholding using type II fuzzy sets," Pattern Recognition, 38, 2363-2372 (2005). [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).
- 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]
- D. Gnanadurai and V. Sadasivam, "Undecimated wavelet based speckle reduction for SAR images," Pattern Recognition Letters, 26, 793-800 (2005). [CrossRef]
- 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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