## Stochastic speckle noise compensation in optical coherence tomography using non-stationary spline-based speckle noise modelling |

Biomedical Optics Express, Vol. 4, Issue 9, pp. 1769-1785 (2013)

http://dx.doi.org/10.1364/BOE.4.001769

Acrobat PDF (5088 KB)

### Abstract

Optical coherence tomography (OCT) allows for non-invasive 3D visualization of biological tissue at cellular level resolution. Often hindered by speckle noise, the visualization of important biological tissue details in OCT that can aid disease diagnosis can be improved by speckle noise compensation. A challenge with handling speckle noise is its inherent non-stationary nature, where the underlying noise characteristics vary with the spatial location. In this study, an innovative speckle noise compensation method is presented for handling the non-stationary traits of speckle noise in OCT imagery. The proposed approach centers on a non-stationary spline-based speckle noise modeling strategy to characterize the speckle noise. The novel method was applied to ultra high-resolution OCT (UHROCT) images of the human retina and corneo-scleral limbus acquired in-vivo that vary in tissue structure and optical properties. Test results showed improved performance of the proposed novel algorithm compared to a number of previously published speckle noise compensation approaches in terms of higher signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR) and better overall visual assessment.

© 2013 OSA

## 1. Introduction

*in vivo*. Furthermore, the data acquisition speed of OCT systems has greatly improved over the past decade with the development of high-speed CCD and CMOS [1

1. B. Potsaid, I. Gorczynska, V. J. Srinivasan, Y. Chen, J. Liu, J. Jiang, A. Cable, J. S. Duker, and J. G. Fujimoto, “Ultrahigh speed spectral / Fourier domain opthalmic OCT imaging,” Proc. SPIE **7163**, 716307 (2009). [CrossRef]

2. T. Klein, W. Wieser, C. M. Eigenwillig, B. R. Biedermann, and R. Huber, “Megahertz OCT for ultrawide-field retinal imaging with a 1050 nm Fourier domain mode-locked laser,” Opt. Express **19**, 3044–3062 (2011). [CrossRef] [PubMed]

*in vivo*imaging of the human eye, gastrointestinal tract, as well as the epidermis and dermis layers of the skin [3

3. W. Drexler and J. Fujimoto, “Biological and medical physics, biomedical engineering,” in *Optical Coherence Tomography: Technology and Applications* (Springer, 2008). [CrossRef]

12. J. Lee, “Speckle suppression and analysis for synthetic aperture radar,” Opt. Eng. **25**, 636–643 (1986). [CrossRef]

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

15. T. Loupas, W. Mcdicken, and P. Allen, “An adaptive weighted median filter for speckle suppression in medical ultrasound images,” IEEE Trans. Circuits Syst. **36**, 129–135 (1989). [CrossRef]

16. A. Wong, A. Mishra, K. Bizheva, and D. A. Clausi, “General Bayesian estimation for speckle noise reduction in optical coherence tomography retinal imagery,” Opt. Express **18**, 8338–8352 (2010). [CrossRef] [PubMed]

17. A. Lopes, E. Nezry, R. Touzi, and H. Laur, “Structure detection and adaptive speckle filtering in SAR images,” Int. J. Remote Sens. **14**, 1735–1758 (1993). [CrossRef]

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

27. R. Touzi, “A review of speckle filtering in the context of estimation theory,” IEEE Trans Geosci. Remote Sens. **40**, 2392–2404 (2002). [CrossRef]

28. J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, “Image denoising using scale mixtures of Gaussians in the wavelet domain,” IEEE Trans. Image Process. **23**, 1338–1351 (2003). [CrossRef]

29. J.-A. Guerrero-Colón, L. Mancera, and J. Portilla, “Image restoration using space-variant Gaussian scale mixtures in overcomplete pyramids,” IEEE Trans. Image Process. **17**, 27–41 (2008). [CrossRef] [PubMed]

16. A. Wong, A. Mishra, K. Bizheva, and D. A. Clausi, “General Bayesian estimation for speckle noise reduction in optical coherence tomography retinal imagery,” Opt. Express **18**, 8338–8352 (2010). [CrossRef] [PubMed]

**Non-stationary speckle noise modeling:**while the previous method assumes stationary speckle characteristics, the proposed method assumes that speckle variance is spatially-varying and estimates it using local Median Absolute Deviation, found to have superior noise estimation performance [31].**Stochastic acceptance-rejection sampling:**while the previous method accepts randomly drawn samples based on a fixed criterion, the NSC method introduces a novel stochastic acceptance-rejection sampling strategy which accepts samples probabilistically based on the local speckle characteristics, thus better adapting to the underlying image information.**Local structure importance-weighted estimation:**while the previous method accepts or rejects samples based on first-order statistics, the NSC approach incorporates more local structure information in its importance-weighting function, thus improving estimation of the posterior.

32. J. A. Fessler, “Tomographic reconstruction using information-weighted spline smoothing,” in *Information Processing in Medical Imaging*,H. H. Barrett and A. F. Gmitro, eds. (Springer BerlinHeidelberg, 1993), pp. 372–386. [CrossRef]

## 2. Methodology

### 2.1. Problem formulation

*G*represents the measurements taken over the domain of

*x̱*,

*F*represents the true reflectance of the sample, and

*N*denotes the speckle noise. Because different tissue types can have very different backscattering properties, some regions naturally produce more speckle. As such,

*N*should be treated as a non-stationary noise process in

*x̱*. By taking the logarithm of the measured data

*G*, the multiplicative relationship between

*F*and

*N*becomes additive, and Eq. (1) becomes Looking at Eq. (2), one can reduce the complexity of estimating the true reflectance of the sample by estimating log

*F*(

*x̱*) rather than

*F*(

*x̱*) itself, and then taking the exponential of the logarithmic estimate.

*p*(log

*F*(

*x̱*)|log

*G*(

*x̱*)), which is intractable to obtain analytically in this case. To tackle this issue, we estimate the posterior

*p*(log

*F*(

*x̱*)|log

*G*(

*x̱*)) using a non-parametric, spatially-adaptive Monte Carlo sampling method. By adapting the posterior estimation process using the novel spline-based speckle model introduced herein, we can better capture the spatially-varying speckle noise characteristics in OCT imagery to aid in the speckle noise compensation process.

### 2.2. Non-stationary spline-based speckle noise model

*N*is a non-stationary noise process due to the varying tissue backscattering properties, one strategy to deal with this is to construct a non-stationary speckle noise model over the domain of

*x̱*. While the speckle noise process

*N*is non-stationary as a whole across the entire set of measurements, it can be reasonably assumed to be stationary within a small region of interest. As such, one can obtain an initial estimate of the speckle noise variance at a pixel

*x̱*based on the local noise statistics. Furthermore, it can be observed that pixels within very close proximity of each other have similar speckle noise characteristics, given that neighboring pixels within an image typically capture connected tissues with similar tissue backscattering properties. As such, one may want to ensure that the speckle noise variances estimated for neighboring pixels are consistent. Motivated by these insights and observations, we introduce a spline-based non-stationary speckle model for characterizing speckle noise variances over the domain of

*x̱*.

*of each pixel by taking the difference of the pixel values with the median pixel value in the neighborhood, and then we find the median of the absolute values of these differences. The MAD can be used to estimate the standard deviation in the log space by multiplying by a constant: The use of MAD for estimating local variance is robust to the presence of outliers, and was shown in a comprehensive analysis of noise estimation strategies to be the most effective at characterizing local noise variance [31].*

_{N}*x̱*given the set of computed local variances within a neighborhood ℵ

*. To help determine the speckle noise variance based on the set of computed local variances, we observe that the local variances that best approximates the noise variance are those computed in areas that are largely homogeneous. Furthermore, we observe that, in general, the most frequently occurring areas within an image are such homogeneous areas. Motivated by these observations, for each pixel*

_{S}*x̱*, we compute the initial noise variance estimate

*M*(

*x̱*) as the mode of the set of computed local variances in the neighborhood ℵ

*: Based on empirical testing, the neighborhoods ℵ*

_{S}*and ℵ*

_{N}*were set to 9×9 and 15×15, respectively, for strong speckle noise variance estimation performance.*

_{S}*M*(

*x̱*) to arrive at the final speckle noise variance estimate

*S*(

*x̱*). Therefore, the spline-based speckle noise variance estimate

*S*(

*x̱*) can be defined as where

*p*is a smoothing parameter and D

^{2}is the second derivative operator. By varying

*p*, the resulting spline will vary between a least-squares straight line fit (

*p*= 0) and a natural cubic spline interpolation (

*p*= 1). Empirical testing led to a choice of 0.004 for

*p*, which provided a good balance between data fidelity and estimation smoothness enforcement.

### 2.3. Spatially-adaptive Monte Carlo posterior estimation

*S*, a spatially-adaptive Monte Carlo approach is then introduced to estimate the posterior

*p*(log

*F*(

*x̱*)|log

*G*(

*x̱*)). We extend upon the concept of importance-weighted Monte Carlo sampling [34

34. M.-H. Chen, “Importance-weighted marginal Bayesian posterior density estimation,” J. Am. Stat. Assoc. **89**, 818–824 (1994). [CrossRef]

*x̱*

_{0}of a pixel of interest, we use a neighborhood around

*x̱*

_{0}as the search space, sampling new pixels uniformly at various values of

*x̱*. The neighborhoods around these samples are examined to determine their statistical similarity to the neighborhood around

_{i}*x̱*

_{0}before the samples are accepted. All the accepted samples and their importance weights are denoted by Ω. Intuitively, we want to accept a sample with high statistical likelihood of being a realization of the posterior

*p*(log

*F*(

*x̱*)|log

*G*(

*x̱*)). The probability of accepting a sample into Ω is

*α*(

*x̱*|

_{i}*x̱*

_{0}), and is calculated by examining the neighboring pixels around each of

*x̱*

_{0}and

*x̱*according to The normalization terms

_{i}*λ*are defined such that

_{j}*α*(

*x̱*|

_{i}*x̱*

_{0}) = 1 if the neighbors around

*x̱*are identical to those around

_{i}*x̱*

_{0}. The measured pixel intensities in log-space at the

*j*location in the neighborhoods around

^{th}*x̱*

_{0}and

*x̱*are

_{i}*h*

_{0}[

*j*] and

*h*[

_{i}*j*], respectively. We assume that neighboring pixels are independent of one another in order to express the total probability as the product of probabilities for each neighbor. It can be observed that Eq. (7) adapts dynamically the likelihood criterion based on

*S*(

*x̱*

_{0}) according to our spline-based speckle noise model.

*α*(

*x̱*|

_{i}*x̱*

_{0}), computing the weighted histogram, and then normalizing so that the area under the histogram is unity. The result is our estimate,

*p̂*(log

*F*(

*x̱*)|log

*G*(

*x̱*)), which can be used to reconstruct log

*F̂*(

*x̱*), as described in Eq. (3).

## 3. Experimental setup

*λc*=1060 nm, Δ

*λ*=110 nm, Pout=10 mW) to provide 3

*μ*m and 6

*μ*m axial resolution in the corneal and retinal tissue respectively. At the detection end, the system was interfaced with a high performance spectrometer (P&P Optica) and a fast InGaAs linear array CCD camera (Sensors Unlimited Inc.) with 1024 pixels and readout rate of 47 kHz. Volumetric images were acquired from the human retina and limbus with 1.3 mW power of the incident imaging beam, which resulted in 95 dB system SNR near the zero delay line. The imaging procedure was carried out in the biomedical optical imaging group at the University of Waterloo in accordance with the University of Waterloo ethics regulations for research involving human subjects. The images selected for testing were chosen because they contain a variety of tissue types with different morphology and optical properties that result in spatially varying speckle noise characteristics; they are well-suited for evaluating the speckle compensation performance of the proposed NSC method. For simplification purposes, the NSC method does not account for speckle correlation.

### 3.1. Experimental OCT imaging data

#### 3.1.1. Experiment 1: healthy human retina

*μ*m and lateral resolution of 15

*μ*m.

#### 3.1.2. Experiment 2: healthy human corneo-scleral limbus

*μ*m and lateral resolution of 15

*μ*m.

#### 3.1.3. Experiment 3: human limbus with pinguecula

*μ*m and lateral resolution of 15

*μ*m.

### 3.2. Quantitative performance metrics

#### 3.2.1. SNR analysis

20. 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]

*μ*and

_{r}*local homogeneous region of interest (ROI), marked by blue boxes in Fig. 1 and*

^{th}*R*denotes the total number of considered ROIs on the OCT image.

#### 3.2.2. CNR analysis

20. 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]

*μ*

_{r}_{1}and

*μ*

_{r}_{2}represent the mean of two different ROIs that are used to obtain the CNR value and marked by numbered red boxes in Fig. 1 and the

*σ*

_{r}_{1}and

*σ*

_{r}_{2}are the corresponding variances for these arbitrary ROIs.

#### 3.2.3. ENL analysis

16. A. Wong, A. Mishra, K. Bizheva, and D. A. Clausi, “General Bayesian estimation for speckle noise reduction in optical coherence tomography retinal imagery,” Opt. Express **18**, 8338–8352 (2010). [CrossRef] [PubMed]

*h*homogeneous region of interest. It is a measure of smoothness in this homogeneous region, where a greater value depicts a more smooth region.

^{th}#### 3.2.4. Edge preservation analysis

35. 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]

^{2}

*V*and ∇

^{2}

*Ĝ*are the Laplacian operator applied to the original image and the noise-free reconstruction respectively; and

^{2}

*V*and ∇

^{2}

*Ĝ*.

## 4. Results

20. 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]

35. 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]

### 4.1. Processed images

### 4.2. Quantitative analysis

#### 4.2.1. SNR analysis

#### 4.2.2. CNR analysis

#### 4.2.3. ENL analysis

#### 4.2.4. Edge preservation analysis

### 4.3. Run time

### 4.4. Visual assessment

## Discussion

## Acknowledgments

## References and links

1. | B. Potsaid, I. Gorczynska, V. J. Srinivasan, Y. Chen, J. Liu, J. Jiang, A. Cable, J. S. Duker, and J. G. Fujimoto, “Ultrahigh speed spectral / Fourier domain opthalmic OCT imaging,” Proc. SPIE |

2. | T. Klein, W. Wieser, C. M. Eigenwillig, B. R. Biedermann, and R. Huber, “Megahertz OCT for ultrawide-field retinal imaging with a 1050 nm Fourier domain mode-locked laser,” Opt. Express |

3. | W. Drexler and J. Fujimoto, “Biological and medical physics, biomedical engineering,” in |

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

5. | J. M. Schmitt, “Array detection for speckle reduction in optical coherence microscopy,” Phys. Med. Biol. |

6. | M. Bashkansky and J. Reintjes, “Statistics and reduction of speckle in optical coherence tomography,” Opt. Lett. |

7. | N. Iftimia, B. E. Bouma, and G. J. Tearney, “Speckle reduction in optical coherence tomography by ‘path length encoded’ angular compounding,” J. Biomed. Opt. |

8. | A. E. Desjardins, B. J. Vakoc, W. Y. Oh, S. M. Motaghiannezam, G. J. Tearney, and B. E. Bouma, “Angle-resolved optical coherence tomography with sequential angular selectivity for speckle reduction,” Opt. Express |

9. | T. M. Jørgensen, 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,” in Optical Coherence Tomography and Coherence Techniques III, vol. 6627 of Proceedings of SPIE-OSA Biomedical Optics, P. Andersen and Z. Chen, eds. (Optical Society of America, 2007), pp. 22. |

10. | D. P. Popescu, M. D. Hewko, and M. G. Sowa, “Speckle noise attenuation in optical coherence tomography by compounding images acquired at different positions of the sample,” Opt. Commun. |

11. | L. Fang, S. Li, Q. Nie, J. A. Izatt, C. A. Toth, and S. Farsiu, “Sparsity based denoising of spectral domain optical coherence tomography images,” Biomed. Opt. Express |

12. | J. Lee, “Speckle suppression and analysis for synthetic aperture radar,” Opt. Eng. |

13. | V. Frost, J. Stiles, K. Shanmugan, and J. Holtzman, “A model for radar images and its application to adaptive digital filtering for multiplicative noise,” IEEE Trans. Pattern Analysis Mach. Intell. |

14. | D. Kuan, A. Sawchuk, T. Strand, and P. Chavel, “Adaptive restoration of images with speckle,” IEEE Trans. Acoust. Speech Signal Process. |

15. | T. Loupas, W. Mcdicken, and P. Allen, “An adaptive weighted median filter for speckle suppression in medical ultrasound images,” IEEE Trans. Circuits Syst. |

16. | A. Wong, A. Mishra, K. Bizheva, and D. A. Clausi, “General Bayesian estimation for speckle noise reduction in optical coherence tomography retinal imagery,” Opt. Express |

17. | A. Lopes, E. Nezry, R. Touzi, and H. Laur, “Structure detection and adaptive speckle filtering in SAR images,” Int. J. Remote Sens. |

18. | 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. |

19. | A. Ozcan, A. Bilenca, A. E. Desjardins, B. E. Bouma, and G. J. Tearney, “Speckle reduction in optical coherence tomography images using digital filtering,” Opt. Lett. |

20. | P. Puvanathasan and K. Bizheva, “Speckle noise reduction algorithm for optical coherence tomography based on interval type II fuzzy set,” Opt. Express |

21. | M. Gargesha, M. W. Jenkins, A. M. Rollins, and D. L. Wilson, “Denoising and 4D visualization of OCT images,” Opt. Express |

22. | Z. Jian, L. Yu, B. Rao, B. J. Tromberg, and Z. Chen, “Three-dimensional speckle suppression in optical coherence tomography based on the curvelet transform,” Opt. Express |

23. | Y. Yu and S. Acton, “Speckle reducing anisotropic diffusion,” Opt. Express |

24. | D. Fernandez, H. Salinas, and C. Puliafito, “Automated detection of retinal layer structures on optical coherence tomography images,” Opt. Express |

25. | R. Bernardes, C. Maduro, P. Serranho, A. Araujo, S. Barberio, and J. Cunha-Vas, “Improved adaptive complex diffusion despeckling filter,” Opt. Express |

26. | D. T. Kuan, A. A. Sawchuk, T. C. Strand, and P. Chavel, “Adaptive noise smoothing filter for images with signal-dependent noise,” IEEE Trans. Pattern Analysis Mach. Intell. |

27. | R. Touzi, “A review of speckle filtering in the context of estimation theory,” IEEE Trans Geosci. Remote Sens. |

28. | J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, “Image denoising using scale mixtures of Gaussians in the wavelet domain,” IEEE Trans. Image Process. |

29. | J.-A. Guerrero-Colón, L. Mancera, and J. Portilla, “Image restoration using space-variant Gaussian scale mixtures in overcomplete pyramids,” IEEE Trans. Image Process. |

30. | A. Buades, B. Coll, and J. M. Morel, “A non-local algorithm for image denoising,” in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Vol. 2 (IEEE, 2005), pp. 60–65. |

31. | A. Leigh, A. Wong, D. A. Clausi, and P. Fieguth, “Comprehensive analysis on the effects of noise estimation strategies on image noise artifact suppression performance,” in Proceedings of IEEE International Symposium on Multimedia(IEEE, 2011), pp. 97–104. |

32. | J. A. Fessler, “Tomographic reconstruction using information-weighted spline smoothing,” in |

33. | P. Fieguth, |

34. | M.-H. Chen, “Importance-weighted marginal Bayesian posterior density estimation,” J. Am. Stat. Assoc. |

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

36. | S. Aja-Fernández and C. Alberola-López, “On the estimation of the coefficient of variation for anisotropic diffusion speckle filtering,” IEEE Trans. Image Process. |

**OCIS Codes**

(030.6140) Coherence and statistical optics : Speckle

(100.2980) Image processing : Image enhancement

(100.3010) Image processing : Image reconstruction techniques

(110.4500) Imaging systems : Optical coherence tomography

(170.4460) Medical optics and biotechnology : Ophthalmic optics and devices

**ToC Category:**

Optical Coherence Tomography

**History**

Original Manuscript: May 24, 2013

Revised Manuscript: July 19, 2013

Manuscript Accepted: July 19, 2013

Published: August 28, 2013

**Citation**

Andrew Cameron, Dorothy Lui, Ameneh Boroomand, Jeffrey Glaister, Alexander Wong, and Kostadinka Bizheva, "Stochastic speckle noise compensation in optical coherence tomography using non-stationary spline-based speckle noise modelling," Biomed. Opt. Express **4**, 1769-1785 (2013)

http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-4-9-1769

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### References

- B. Potsaid, I. Gorczynska, V. J. Srinivasan, Y. Chen, J. Liu, J. Jiang, A. Cable, J. S. Duker, and J. G. Fujimoto, “Ultrahigh speed spectral / Fourier domain opthalmic OCT imaging,” Proc. SPIE7163, 716307 (2009). [CrossRef]
- T. Klein, W. Wieser, C. M. Eigenwillig, B. R. Biedermann, and R. Huber, “Megahertz OCT for ultrawide-field retinal imaging with a 1050 nm Fourier domain mode-locked laser,” Opt. Express19, 3044–3062 (2011). [CrossRef] [PubMed]
- W. Drexler and J. Fujimoto, “Biological and medical physics, biomedical engineering,” in Optical Coherence Tomography: Technology and Applications (Springer, 2008). [CrossRef]
- J. Rogowska and M. E. Brezinski, “Evaluation of the adaptive speckle suppression filter for coronary optical coherence tomography imaging,” 19, 1261–1266 (2000).
- J. M. Schmitt, “Array detection for speckle reduction in optical coherence microscopy,” Phys. Med. Biol.42, 1427–1439 (1997). [CrossRef] [PubMed]
- M. Bashkansky and J. Reintjes, “Statistics and reduction of speckle in optical coherence tomography,” Opt. Lett.25, 545–547 (2000). [CrossRef]
- N. Iftimia, B. E. Bouma, and G. J. Tearney, “Speckle reduction in optical coherence tomography by ‘path length encoded’ angular compounding,” J. Biomed. Opt.8, 260–263 (2003). [CrossRef] [PubMed]
- A. E. Desjardins, B. J. Vakoc, W. Y. Oh, S. M. Motaghiannezam, G. J. Tearney, and B. E. Bouma, “Angle-resolved optical coherence tomography with sequential angular selectivity for speckle reduction,” Opt. Express15, 6200–6209 (2007). [CrossRef] [PubMed]
- T. M. Jørgensen, 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,” in Optical Coherence Tomography and Coherence Techniques III, vol. 6627 of Proceedings of SPIE-OSA Biomedical Optics, P. Andersen and Z. Chen, eds. (Optical Society of America, 2007), pp. 22.
- D. P. Popescu, M. D. Hewko, and M. G. Sowa, “Speckle noise attenuation in optical coherence tomography by compounding images acquired at different positions of the sample,” Opt. Commun.269, 247–251 (2007). [CrossRef]
- L. Fang, S. Li, Q. Nie, J. A. Izatt, C. A. Toth, and S. Farsiu, “Sparsity based denoising of spectral domain optical coherence tomography images,” Biomed. Opt. Express3, 927–942 (2012). [CrossRef] [PubMed]
- J. Lee, “Speckle suppression and analysis for synthetic aperture radar,” Opt. Eng.25, 636–643 (1986). [CrossRef]
- V. Frost, J. Stiles, K. Shanmugan, and J. Holtzman, “A model for radar images and its application to adaptive digital filtering for multiplicative noise,” IEEE Trans. Pattern Analysis Mach. Intell.4, 157–166 (1982). [CrossRef]
- D. Kuan, A. Sawchuk, T. Strand, and P. Chavel, “Adaptive restoration of images with speckle,” IEEE Trans. Acoust. Speech Signal Process.35, 373–383 (1987). [CrossRef]
- T. Loupas, W. Mcdicken, and P. Allen, “An adaptive weighted median filter for speckle suppression in medical ultrasound images,” IEEE Trans. Circuits Syst.36, 129–135 (1989). [CrossRef]
- A. Wong, A. Mishra, K. Bizheva, and D. A. Clausi, “General Bayesian estimation for speckle noise reduction in optical coherence tomography retinal imagery,” Opt. Express18, 8338–8352 (2010). [CrossRef] [PubMed]
- A. Lopes, E. Nezry, R. Touzi, and H. Laur, “Structure detection and adaptive speckle filtering in SAR images,” Int. J. Remote Sens.14, 1735–1758 (1993). [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,” Opt. Lett.24, 1901–1910 (2007).
- P. Puvanathasan and K. Bizheva, “Speckle noise reduction algorithm for optical coherence tomography based on interval type II fuzzy set,” Opt. Express15, 15747–15758 (2007). [CrossRef] [PubMed]
- M. Gargesha, M. W. Jenkins, A. M. Rollins, and D. L. Wilson, “Denoising and 4D visualization of OCT images,” Opt. Express16, 12313–12333 (2008). [CrossRef] [PubMed]
- Z. Jian, L. Yu, B. Rao, B. J. Tromberg, and Z. Chen, “Three-dimensional speckle suppression in optical coherence tomography based on the curvelet transform,” Opt. Express18, 1024–1032 (2010). [CrossRef] [PubMed]
- Y. Yu and S. Acton, “Speckle reducing anisotropic diffusion,” Opt. Express11, 1260–1270 (2002).
- D. Fernandez, H. Salinas, and C. Puliafito, “Automated detection of retinal layer structures on optical coherence tomography images,” Opt. Express13, 10200–10216 (2005). [CrossRef]
- R. Bernardes, C. Maduro, P. Serranho, A. Araujo, S. Barberio, and J. Cunha-Vas, “Improved adaptive complex diffusion despeckling filter,” Opt. Express18, 24048–24059 (2010). [CrossRef] [PubMed]
- D. T. Kuan, A. A. Sawchuk, T. C. Strand, and P. Chavel, “Adaptive noise smoothing filter for images with signal-dependent noise,” IEEE Trans. Pattern Analysis Mach. Intell.7, 165–177 (1985). [CrossRef]
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