College of Computer Science and Technology, Wuhan University of Science and Technology, Wuhan, Hubei, China

Key Laboratory of Molecular Biophysics of the Ministry of Education, College of Life Science and Technology, Huazhong University of Science and Technology, Wuhan, Hubei, China

School of Technology, Michigan Technological University, 1400 Townsend Drive, Houghton, Michigan 49931-1295, USA

Rush University Cancer Center, Rush University Medical Center, Chicago, Illinois 60612, USA

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.

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

Different methods have been investigated for speckle reduction. These methods include early methods such as Lee filter

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

Experimental results for speckle reduction

We performed several experiments to test the performance of the proposed method. In the experiments, the ultrasound images used were from cattle's follicles. Figure

Experimental results of different methods on a cattle's follicle ultrasound image

**Experimental results of different methods on a cattle's follicle ultrasound image**. (a) Original image, (b) result with SRAD, (c) result with DPAD, (d) result with RDPAD, (e) result with nonlocal means. The number of iterations is 300 in (b), (c) and (d).

Experimental results of different methods on another cattle's follicle ultrasound image

**Experimental results of different methods on another cattle's follicle ultrasound image**. (a) Original image with a line overlapped, (b) result with SRAD, (c) result with DPAD, (d) result with RDPAD. The number of iterations is 300 in (b), (c) and (d).

Experimental results in respect of detail preserving for different methods over a horizontal scan line (row 65) of the ultrasound image in Fig.2 (a)

**Experimental results in respect of detail preserving for different methods over a horizontal scan line (row 65) of the ultrasound image in Fig.2 (a)**. (a) Result with DPAD, (b) result with proposed RDPAD.

Results of different methods with respect to the number of iterations on an image shown in Fig.2 (a)

**Results of different methods with respect to the number of iterations on an image shown in Fig.2 (a)**. The first column displays the results obtained by SRAD, the second column displays the results obtained by DPAD, and the third column obtained by for RDPAD. The number of iterations is 50, 100, 300, 500 and 1000 corresponding to rows 1 to 5, respectively.

In order to compare the effectiveness of speckle reduction on segmentation, we used active contour without edge (ACWE) developed in

Segmentation results with different speckle reduction methods

**Segmentation results with different speckle reduction methods**. (a) Original image with manual segmentation, (b) segmentation result with SRAD, (c) segmentation result with DPAD, (d) segmentation result with RDPAD, (e) segmentation result with nonlocal means.

Quantitative comparison of speckle reduction methods

For quantitative comparison, we used the measurement developed in _{w }

where the local contrast at pixel (

where

Homogeneous region and a set of edge points used to calculate RC value

**Homogeneous region and a set of edge points used to calculate RC value**. (a) Homogeneous region, (b) set of edge points.

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

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

Methods

Previous work on anisotropic diffusion for speckle reduction

Anisotropic diffusion was proposed in

where ∇ is the gradient operator,

In the study of anisotropic diffusion for speckle reduction, a lot of research focuses on the development of the computation of

where

is called instantaneous coefficient of variation (ICOV).

In fact, SRAD is obtained by combining anisotropic diffusion with Lee filter

and the diffusion coefficient function adopted by DPAD is

Besides Aja-Fernandez's work, Tauber et al.

as the diffusion coefficient function. He used the same way as SRAD to compute the coefficient of variation but different diffusion coefficient function. The diffusion coefficient function in (8) is from

The diffusion coefficient function in (9) allows the neighbours with larger gradient magnitude than _{e }

Inspired by their success

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

Computation of instantaneous coefficient of variation with a new scheme

In SRAD and DPAD, coefficient of variation is adopted to distinguish homogeneous regions from edges. However, the computation of coefficient of variation from 3 × 3 neighbour is not robust ** v**0,..

Estimation windows

**Estimation windows**. (a) 5 × 5 square window used by Aja-Fernandez et al. (b) Modified 5 × 5 window used by the proposed RDPAD.

Robust DPAD diffusion function (RDPAD)

Now let's introduce robust DPAD (RDPAD). Starting from equation (9), we have:

Let

Using equation (9) and equation (12), we can obtain a new computation of c(q), which can be expressed as follows:

The above equation can be rewritten as

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

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.

Competing interests

The authors declare that they have no competing interests.

Authors' contributions

XL, JL, LC, XX and JT were involved in the methods design. XL, JL, LC were involved with methods development, coordination and data collection. XL, XX, LC and YD were involved with data analysis. XL, JL, LC, XX are responsible for the writing of manuscript and JT revised some parts of the paper based on the original paper.

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.