# A robust detail preserving anisotropic diffusion for speckle reduction in ultrasound images

- Xiaoming Liu
^{1}, - Jun Liu
^{1}, - Xin Xu
^{1}, - Lei Chun
^{2}Email author, - Jinshan Tang
^{1, 3}Email author and - Youping Deng
^{4}

**12(Suppl 5)**:S14

https://doi.org/10.1186/1471-2164-12-S5-S14

© Lui et al. licensee BioMed Central Ltd 2011

**Published: **23 December 2011

## Abstract

### Background

Speckles in ultrasound imaging affect image quality and can make the post-processing difficult. Speckle reduction technologies have been employed for removing speckles for some time. One of the effective speckle reduction technologies is anisotropic diffusion. Anisotropic diffusion technology can remove the speckles effectively while preserving the edges of the image and thus has drawn great attention from image processing scientists. However, the proposed methods in the past have different disadvantages, such as being sensitive to the number of iterations or low capability of preserving the details of the ultrasound images. Thus a detail preserved anisotropic diffusion speckle reduction with less sensitive to the number of iterations is needed. This paper aims to develop this kind of technologies.

### Results

In this paper, we propose a robust detail preserving anisotropic diffusion filter (RDPAD) for speckle reduction. In order to get robust diffusion, the proposed method integrates Tukey error norm function into the detail preserving anisotropic diffusion filter (DPAD) developed recently. The proposed method could prohibit over-diffusion and thus is less sensitive to the number of iterations

### Conclusions

The proposed anisotropic diffusion can preserve the important structure information of the original image while reducing speckles. It is also less sensitive to the number of iterations. Experimental results on real ultrasound images show the effectiveness of the proposed anisotropic diffusion filter.

## Keywords

## Background

Medical imaging techniques have obtained great development in the past decades and have been found different applications in disease diagnosis. One of these important imaging techniques is ultrasound imaging. ultrasound imaging has many advantages such as noninvasiveness, portability, and low price, which make it attractive to different clinical applications [1]. However, the quality of ultrasound images is greatly affected by speckles, a granular pattern formed due to coherent interferences of backscattered echoes from the scatters [2]. The presence of speckle degrades the quality of ultrasound images, and thus affects diagnosis. Thus, speckle reduction has become an important task in many applications with ultrasound imaging.

Different methods have been investigated for speckle reduction. These methods include early methods such as Lee filter [3], Frost filter [4], Kuan filter [5], and recently developed methods such as adaptive filters [6, 7], wavelet transform [8–11], bilateral filters [12], nonlocal-means [13] and anisotropic diffusion filters [14–18], etc. In [6], an adaptive weighted median filter (AWMF) for speckle reduction is proposed. Different from the common median filter, AWMF adjusts weight coefficients and smoothing characteristics based on the local statistics. In [7], an adaptive speckle suppression filter (ASSF) is developed for speckle reduction in B-scan images. The proposed filter used appropriately shaped and sized local filtering kernels and has better adaptation to local variations. In [9], a speckle suppression method is presented for ultrasound images. In the presented method, the original image was first logarithmically transformed, and then 2-D wavelet transform was applied to obtain multiscale decomposition for speckle reduction. Besides the methods described above, anisotropic diffusion filters [14] have been studied deeply in recent years [15–23]. In [15], an anisotropic diffusion method which integrated with the Smallest Univalue Segment Assimilating Nucleus (SUSAN) edge detector was proposed. The proposed method can provide good performance in both speckle reduction and detail preservation. In [16], a nonlinear coherent diffusion (NCD) model for logarithmic compressed B-mode ultrasound images was developed. The proposed method can work in real-time. In [18], Yu *et al.* proposed the speckle reducing anisotropic diffusion (SRAD) method for ultrasonic images. The method integrated spatially adaptive filter into the diffusion technique, and exploited the instantaneous coefficient of variation for edge detection. Compared with previous method, the method has better performance in both edge preservation and speckle reduction. In addition, the SRAD has been further applied to 3D ultrasound images [19, 20] and also obtained good performance. Recently, another improvement for anisotropic diffusion filter is the work in [23]. In [23], Tauber *et al.* improved the robustness of the original SRAD by following the analysis of P-M method with respect to the robust estimation of a piecewise smooth image. Inspired by the success of the work [17, 23], we will further improve the robustness of the DPAD in this paper.

## Results

In order to test the performance of the proposed method, we have performed several experiments on ultrasound images. The proposed method was compared with the SRAD algorithm [18] developed by Yu and the DPAD algorithm developed by Aja-Fernandez [22].

### Experimental results for speckle reduction

### Quantitative comparison of speckle reduction methods

*C*

_{ w }in an image

*I*is defined as [25]:

*x*,

*y*),

*c*(

*x*,

*y*) is defined as

*I*(

*x*,

*y*) is an image pixel intensity value,

*w*is a region of image (or a set of points), and

*m*is the number of pixels in the region

*w*over which the contrast is evaluated. In the experiments, we selected manually a homogeneous region and a set of edge points for measuring the performance of each method, which is shown in Figure 6. Table 1 shows the RC values from the selected homogeneous region and the selected set of edge points. Based on Table 1, SRAD and DPAD can reduce the speckles in the selected homogeneous region effectively, but the CR values of the selected set of edge points are reduced. However, the proposed method can preserve the contrast of the edge points and can remove the speckle in the homogenous region effectively.

Region contrast (RC) values of different speckle reduction methods

Regions | Original image | SRAD | DPAD | RDPAD |
---|---|---|---|---|

Homogenous region | 3.4971 | 0.0041 | 0.0041 | 0.0046 |

Edge points | 2.9330 | 0.0080 | 0.0109 | 2.8597 |

## Discussion

The proposed speckle reduction can be applied as a preprocessing step for image segmentation [24]. Because ultrasound image segmentation will be affected by speckles, a good speckle reduction method will enhance the performance of image segmentation. Although we have shown some improvement of segmentation after speckle reduction, the number of cases is not big, thus our future work will focus on measuring the performance of speckle reduction on segmentation using large set of ultrasound images.

Another potential application is the extension of the proposed method to 3-D speckle reduction in ultrasound images. As is well known, 3-D ultrasound imaging is a more challenging area than 2-D ultrasound imaging. Based on our current experiments, we predict the proposed method can also get good results for 3-D ultrasound images.

## Conclusion

By integrating the detail preserving anisotropic diffusion developed by Aja-Fernandez and the diffusion coefficient function from [17], we developed a new anisotropic diffusion filter which can have better performance in edge preservation and speckle reduction. Due to the favorable property of "edge-stopping" diffusion, the proposed method is less sensitive to the number of iterations. Experimental results on real ultrasound images indicated that the proposed method can achieve better performance than both SRAD and DPAD. The proposed method provides a preprocessing method for ultrasound image segmentation.

## Methods

### Previous work on anisotropic diffusion for speckle reduction

where ∇ is the gradient operator, *div* is the divergence operator, |•| is the magnitude.

*c*(

*x*). One of the methods is speckle reducing anisotropic diffusion filter developed by Yu and Acton [18]. In [18], they proposed the following equation to compute the diffusion coefficients:

is called instantaneous coefficient of variation (ICOV).

The diffusion coefficient function in (9) allows the neighbours with larger gradient magnitude than *σ*_{
e
} has no influence on the current pixel. The method can preserve sharper edges than previous formulations.

Inspired by their success [17, 22, 23], in this paper, we aim to improve the robustness of DPAD algorithm and develop a modified algorithm with both advantages from DPAD and Tauber' algorithm [23]. The modified algorithm will preserve sharper edges and be less sensitive to the iteration times.

### The proposed robust detail preserving anisotropic diffusion

In this section, we will develop a new scheme to compute the instantaneous coefficient of variation, and then we introduce the new technique which combines the DPAD algorithm and the diffusion coefficient function in equation (9) from [17]. The proposed method will have the advantages of being robust to outliers (the edges of the image) and less sensitive to the number of diffusion iterations.

#### Computation of instantaneous coefficient of variation with a new scheme

*q*(

*i*,

*j*;

*t*). However, the computation using 5 by 5 neighbours is a little costive. In order to make the diffusion robust and less costive, we propose a new scheme to compute

*q*(

*i*,

*j*;

*t*). The new scheme is shown in Figure 7(b). Let the pixels be v 0,.. v

_{12}as shown in the Figure 7, (8) can be reformulated as:

#### Robust DPAD diffusion function (RDPAD)

In equation (14), we assigns zero weights to the outliers (edges can be seen as outliers in an image) when the instantaneous coefficients of variation is larger than$\frac{2{q}_{0}{\left(t\right)}^{2}}{\left|1-{q}_{0}{\left(t\right)}^{2}\right|}$. However, a decreasing small positive weight is assigned to outliers in Aja-Fernandez's algorithm. Therefore, although both of the proposed method and Aja-Fernandez's method perform diffusion similarly when *q* is small. The behaviour of the two methods will be different when q is large. In the case of large q, the proposed method will stop diffusion while Aja-Fernandez will still perform diffusion. Thus the proposed method can result in sharper edges than Aja-Fernandez's method and the proposed method is also robust to the diffusion iterations.

The proposed anisotropic diffusion can be implemented numerically using the similar way to SRAD, the only difference lies in that the computation of c(q) is different.

## Declarations

### Acknowledgements

The paper is supported by NSFC 61003127, NSF of Hubei Province (NO. 2008CDB345), Educational Commission of Hubei Province (NO.Q20101101) Department of Science and Technology of Hubei Province (NO. D20091102), and Science Foundation of Wuhan University of Science and Technology Project 2008TD04.

## Authors’ Affiliations

## References

- Dhawan AP: Medical image analysis. 2011, Wiley-IEEE Press, 31:View ArticleGoogle Scholar
- Burckhardt C: Speckle in ultrasound B-mode scans. IEEE Transactions on Sonics and Ultrasonics. 1978, 25 (1): 1-6. 10.1109/T-SU.1978.30978.View ArticleGoogle Scholar
- Lee J: Refined filtering of image noise using local statistics. Computer Graphics and Image Processing. 1981, 15 (4): 380-389. 10.1016/S0146-664X(81)80018-4.View ArticleGoogle Scholar
- Frost V, Stiles J, Shanmugan K, Holtzman J: A model for radar images and its application to adaptive digital filtering of multiplicative noise. IEEE Trans Patt Anal Mach Intell. 1982, 4: 157-166. 10.1109/TPAMI.1982.4767223.View ArticleGoogle Scholar
- Kuan D, Sawchuk A, Strand T, Chavel P: Adaptive restoration of images with speckle. IEEE Transactions on Acoustics, Speech and Signal Processing. 1987, 35 (3): 373-383. 10.1109/TASSP.1987.1165131.View ArticleGoogle Scholar
- Loupas T, McDicken WN, Allan PL: An adaptive weighted median filter for speckle suppression in medical ultrasonic images. Circuits and Systems, IEEE Transactions on. 1989, 36 (1): 129-135. 10.1109/31.16577.View ArticleGoogle Scholar
- Karaman M, Kutay MA, Bozdagi G: An adaptive speckle suppression filter for medical ultrasonic imaging. IEEE Trans Med Imaging. 1995, 14 (2): 283-292. 10.1109/42.387710.View ArticlePubMedGoogle Scholar
- Zong X, Laine AF, Geiser EA: Speckle reduction and contrast enhancement of echocardiograms via multiscale nonlinear processing. IEEE Trans Med Imaging. 1998, 17 (4): 532-540. 10.1109/42.730398.View ArticlePubMedGoogle Scholar
- Achim A, Bezerianos A, Tsakalides P: Novel Bayesian multiscale method for speckle removal in medical ultrasound images. IEEE Trans Med Imaging. 2001, 20 (8): 772-783. 10.1109/42.938245.View ArticlePubMedGoogle Scholar
- Pizurica A, Philips W, Lemahieu I, Acheroy M: A versatile wavelet domain noise filtration technique for medical imaging. IEEE Trans Med Imaging. 2003, 22 (3): 323-331. 10.1109/TMI.2003.809588.View ArticlePubMedGoogle Scholar
- Zhang F, Yoo Y, Koh L, Kim Y: Nonlinear diffusion in laplacian pyramid domain for ultrasonic speckle reduction. IEEE Trans Med Imaging. 2007, 26 (2): 200-211. 10.1109/TMI.2006.889735.View ArticlePubMedGoogle Scholar
- Tang J, Guo S, Sun Q, Deng Y, Zhou D: Speckle reducing bilateral filter for cattle follicle segmentation. BMC Genomics. 2010, 11 (Suppl 2): S9-10.1186/1471-2164-11-S2-S9.View ArticleGoogle Scholar
- Coupé P, Hellier P, Kervrann C, Barillot C: Nonlocal means-based speckle filtering for ultrasound images. Image Processing, IEEE Transactions on. 2009, 18 (10): 2221-2229. 10.1109/TIP.2009.2024064.View ArticleGoogle Scholar
- Perona P, Malik J: Scale-space and edge detection using anisotropic diffusion. IEEE Trans Patt Anal Mach Intell. 1990, 12 (7): 629-639. 10.1109/34.56205.View ArticleGoogle Scholar
- Yu J, Tan J, Wang Y: Ultrasound speckle reduction by a SUSAN-controlled anisotropic diffusion method. Pattern Recognition. 2010, 43 (9): 3083-3092. 10.1016/j.patcog.2010.04.006.View ArticleGoogle Scholar
- Abd-Elmoniem KZ, Youssef A, Kadah YM: Real-time speckle reduction and coherence enhancement in ultrasound imaging via nonlinear anisotropic diffusion. IEEE Trans Biomed Eng. 2002, 49 (9): 997-1014. 10.1109/TBME.2002.1028423.View ArticlePubMedGoogle Scholar
- Black M, Sapiro G, Marimont D, Heeger D: Robust anisotropic diffusion. IEEE Trans Image Process. 1998, 7 (3): 421-432. 10.1109/83.661192.View ArticlePubMedGoogle Scholar
- Yu Y, Acton S: Speckle reducing anisotropic diffusion. IEEE Trans Image Process. 2002, 11 (11): 1260-1270. 10.1109/TIP.2002.804276.View ArticlePubMedGoogle Scholar
- Sun Q, Hossack J, Tang J, Acton S: Speckle reducing anisotropic diffusion for 3D ultrasound images. Comput Med Imaging Graph. 2004, 28 (8): 461-470. 10.1016/j.compmedimag.2004.08.001.View ArticlePubMedGoogle Scholar
- Tang J, Sun Q: A 3-D anisotropic diffusion filter for speckle reduction in 3-D ultrasound images. 2009. 2009, 72390T-Google Scholar
- Krissian K, Westin C, Kikinis R, Vosburgh K: Oriented speckle reducing anisotropic diffusion. IEEE Trans Image Process. 2007, 16 (5): 1412-1424. 10.1109/TIP.2007.891803.View ArticlePubMedGoogle Scholar
- Aja-Fernandez S, Alberola-Lopez C: On the estimation of the coefficient of variation for anisotropic diffusion speckle filtering. IEEE Trans Image Process. 2006, 15 (9): 2694-2701. 10.1109/TIP.2006.877360.View ArticlePubMedGoogle Scholar
- Tauber C, Batatia H, Ayache A: A robust speckle reducing anisotropic diffusion. International Conference on Image Processing: 24-27 Oct. 2004 2004. 2004, 247-250.View ArticleGoogle Scholar
- Chan TF, Vese LA: Active contours without edges. IEEE Trans Image Process. 2001, 10 (2): 266-277. 10.1109/83.902291.View ArticlePubMedGoogle Scholar
- Tang J, Liu X, Sun Q: A direct image contrast enhancement algorithm in the wavelet domain for screening mammograms. IEEE Journal of Selected Topics in Signal Processing. 2009, 3 (1): 74-80. 10.1109/JSTSP.2008.2011108.View ArticleGoogle Scholar

## Copyright

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.