Subspace-based technique for speckle noise reduction in ultrasound images
- Norashikin Yahya^{1}Email author,
- Nidal S Kamel^{1} and
- Aamir S Malik^{1}
https://doi.org/10.1186/1475-925X-13-154
© Yahya et al.; licensee BioMed Central Ltd. 2014
Received: 11 September 2014
Accepted: 7 November 2014
Published: 25 November 2014
Abstract
Background and purpose
Ultrasound imaging is a very essential technique in medical diagnosis due to its being safe, economical and non-invasive nature. Despite its popularity, the US images, however, are corrupted with speckle noise, which reduces US images qualities, hampering image interpretation and processing stage. Hence, there are many efforts made by researches to formulate various despeckling methods for speckle reduction in US images.
Methods
In this paper, a subspace-based speckle reduction technique in ultrasound images is proposed. The fundamental principle of subspace-based despeckling technique is to convert multiplicative speckle noise into additive via logarithmic transformation, then to decompose the vector space of the noisy image into signal and noise subspaces. Image enhancement is achieved by nulling the noise subspace and estimating the clean image from the remaining signal subspace. Linear estimation of the clean image is derived by minimizing image distortion while maintaining the residual noise energy below some given threshold. The real US data for validation purposes were acquired under the IRB protocol (200210851-7) at the University of California Davis, which is also consistent with NIH requirements.
Results
Experiments are carried out using a synthetically generated B-mode ultrasound image, a computer generated cyst image and real ultrasound images. The performance of the proposed technique is compared with Lee, homomorphic wavelet and squeeze box filter (SBF) in terms of noise variance reduction, mean preservation, texture preservation and ultrasound despeckling assessment index (USDSAI). The results indicate better noise reduction capability with the simulated images by the SDC than Lee, Wavelet and SBF in addition to less blurry effect. With the real case scenario, the SDC, Lee, Wavelet and SBF are tested with images obtained from raw radio frequency (RF) data. Results generated using real US data indicate that, in addition to good contrast enhancement, the autocorrelation results shows better preservation of image texture by SDC than Lee, Wavelet and SBF.
Conclusion
In general, the performance of the SDC filter is better than Lee, Wavelet and SBF in terms of noise reduction, improvement in image contrast and preservation of the autocorrelation profiles. Furthermore, the filter required less computational time compared to Lee, Wavelet and SBF, which indicates its suitability for real time application.
Keywords
Introduction
Ultrasound (US) imaging is one of the most commonly used medical imaging due for diagnostic purposes to its many advantages such as portability, the noninvasive nature, relatively low cost and presents no radiation risk to patient. These features have made the US imaging as the most prevalent diagnostic tool for health practitioners over other more sophisticated imaging techniques such as CT scan, MRI or PET. Unfortunately, like SAR, US images exhibit a speckle pattern and its statistical model is identical to single-look SAR amplitude signals. Speckle in ultrasound has adverse effect in such a way it causes reduction in image contrast resolution. In [1], Bamber and Daft show that speckle in US images cause reduction of lesion detectability by approximately a factor of eight.
An US machine works by introducing into the body of interest a low-energy pulse of sound with frequencies typically between 3 and 30MHz by a transducer probe that touches the patients’ skin surface. Upon travelling through the body tissue, some of the pulses get attenuated while some small portion of the pulse energy are scattered back to the probe. The scattered pulse is then received by the same probe to produce echo signals which are processed to form two-dimensional images, also known as sonogram. This two-dimensional anatomical maps are called B-mode (brightness) images [2].
In principle, US images provide information about internal tissue structures which resulted from interaction between anatomical tissues with the transmitted ultrasound pulse. Due to interaction between ultrasound waves with tissue, backscattered echo signals are produced, in the form of reflection, scattering, interference and absorption. These echo, resulted from coherent summation of ultrasound scatterers, carry information about the tissue under investigation. The nature of coherent summation of such signals gives rise to an interference pattern known as speckle [3].
The despeckling techniques applied in US and SAR imagery can be classified into four main groups, namely, linear and non-linear filters, adaptive speckle filters, wavelet-based filters and anisotropic diffusion-based (AD) approach. In linear filtering technique [4, 5], the multiplicative speckle noise is first converted into an additive noise by applying logarithmic transformation to the speckled image followed by a Wiener filter in order to reject the resultant additive noise. The despeckled image is fully recovered by applying exponential transformation onto the output of Wiener filter. The technique, which convert the multiplicative speckle noise into an additive one, are commonly referred as homomorphic despeckling methods. The Wiener filter is the oldest approach to image denoising, is optimal in the sense of minimum mean-square error (MSE) and is space invariant linear estimator of the signal for images degraded by additive white noise.
The nonlinear filters are possible alternative to the standard linear filters, and the most popular one is the median filter. It has the advantage of preserving edges and is very effective at removing impulsive noise. The median filter sorts the intensities in the neighbourhood window of the reference pixel and calculates the median value of the sorted data. The denoised pixel is obtained by replacing the original reference pixel value by the median value calculated for the particular neigbourhood window [6–8]. The main problem is that the median filter would blur edges and tiny details.
Wavelet-based denoising techniques continue to generate great interest among the computer vision and image processing community. Some of the proposed wavelet-based speckle filters are presented in [9–15]. The success of the technique is due to the fact that in the wavelet domain, the noise is uniformly spread throughout the coefficients, while most of the image information is concentrated in few significant ones. In other word, the wavelet-transformed images tend to be sparse and consequently, noise removal can be achieved by properly suppressing or thresholding the small coefficients that are likely due to noise. The wavelet-based denoising techniques involve three major steps, 1) perform a 2-D wavelet transform, 2) modify the noisy coefficients using a shrinkage function, and 3) perform a 2-D inverse wavelet transform [16, 17]. In general, the most critical step in wavelet denoising techniques is the modification of wavelet coefficients. The classification of the different type of wavelet denoising is typically based on it different approach in modifying the noisy coefficients.
The adaptive speckle reducing filters such as Lee, Kuan and Frost can be applicable to both US and SAR images. The methods are developed based on multiplicative model of speckle noise. The methods are based on two assumptions, 1) the recorded image and the speckle noise are statistical independence [18], and 2) a constant ratio of noise standard deviation to mean throughout the image. The second assumption is valid in homogeneous regions. Each of these filters achieved speckle reduction via spatial filtering in a square-moving window known as kernel. The filtering is based on the statistical relationship between the centre pixel and its surrounding pixels within a processing window. The typical window size are 3×3, 5×5, and 7×7. With the window-based techniques, the selection of window will greatly affects the quality of the processed image. If the window is too small, the noise filtering algorithm is not effective, where as if the window is too large, subtle details of the image will be lost in the filtering process.
The squeeze box filter (SBF) which can be classified as an iterative technique, reduces speckle noise by suppressing outliers as a local mean of its neighborhood [19, 20]. Based on the fact that speckle is a stochastic process where outliers inevitably occurs, the proposed SBF achieves noise reduction by iteratively removes the outliers. Specifically, the image pixel outliers are defined to be local minimums and local maximums determined from a 3×3 window. Each outlier will be replaced by a local mean determined from a window centered on the outlying pixel. The outlier pixel value is not used in computing the local mean. After all the outliers are replaced by the local means, the process is repeated until a predetermined number of iteration is reached or until convergence is attained. In [19], experimental results showed that the SBF improves the image quality in terms of contrast enhancement, structural similarity and segmentation result. Although an effective speckle reduction, the SBF however still has artifacts in the form of blurred edges and irregular intensity pattern around edges [21].
In this paper, a subspace-based technique to reduce the speckle noise in US images, is proposed. Fundamentally, the proposed technique is an extension of the original work of Ephraim and Van Trees [22], in speech enhancement towards 2-dimensional signals. The underlying principle is to decompose the vector space of the noisy image into a signal-plus-noise subspace and the noise subspace. The noise removal is achieved by nulling the noise subspace and controlling the noise distribution in the signal subspace. For white noise, the subspace decomposition can theoretically be performed by applying the Karhunen-Loeve transform (KLT) to the noisy image. Linear estimator of the clean image is performed by minimizing image distortion while maintaining the residual noise energy below some given threshold. For colored noise, a prewhitening approach prior to KLT transform, or a generalized subspace for simultaneous diagonalization of the clean and noise covariance matrices, can be used. The fundamental signal and noise model for subspace methods is additive noise uncorrelated with the signal. But, in US images the noise is multiplicative in nature, so a homomorphic framework takes advantage of logarithmic transformation, in order to convert multiplicative noise into additive noise.
The paper is organized as follows. Firstly, the statistic of speckle noise in US images is described. Secondly, the principle of subspace and how it can be extended to speckle noise removal is presented. In specific, this second section covers the proposed subspace technique and its implementation in speckle noise filtering followed by experimental results to determine optimum value of Lagrange multiplier. The subsequent section presents the experimental results to validate and evaluate the performance of the proposed filter. The performance evaluation of the proposed technique is divided into three main categories, 1) using simulated B-mode US images 2) using Field II generated images and 3)using real US images in comparison to Lee filter, wavelet filter [23, 24] in homomorphic framework and SBF technique [19]. The final section concludes this paper.
For clarity, an attempt has been made to adhere to a standard notational convention. Lower case boldface characters will generally refer to vectors. Upper case characters will generally refer to matrices. Vector or matrix transposition will be denoted using (.)^{ T } and ${\mathbb{R}}^{m\times m}$ denotes the real vector space of m×m dimensions.
Signal and noise model in ultrasound images
where Y,X and N are the logarithms of G,W and ξ _{ m } respectively.
The subspace-based techniques for noise reduction
where σ is a positive constant.
In the implementation of SDC, a proper selection of signal subspace dimension r and Lagrangian multiplier, λ are critical in order to achieve the best noise reduction technique. For subspace dimension, a method based on eigenvalues is proposed in [31, 32] whereas the Lagrangian multiplier is to be empirically determined. As with any other noise filtering technique, the value noise variance needs to be estimated. In this case, the noise variance can be estimated using the last trailing end of the smallest singular value as outlined in [31].
- 1.
Apply the homomorphic transformation to the noisy image, Y= log(G).
- 2.
Estimate the noise variance, ${v}_{n}^{2}$.
- 3.
Compute the dimension of signal subspace, r.
- 4.
Using the estimated r in step 3, apply eigendecomposition on ${R}_{{Y}_{l}}$, then extract the basis vectors of signal subspace U _{1}, and their related eigenvalues ${\Delta}_{X}^{\left(i\right)}={\Delta}_{Y}^{\left(i\right)}-{v}_{n}^{2}$.
- 5.Select the best value of λ, then compute the optimum linear estimator,${H}_{\mathit{\text{SDC}}}={U}_{1}{\Delta}_{X1}{\left({\Delta}_{X1}+\lambda {v}_{n}^{2}I\right)}^{-1}{U}_{1}^{T}.$(19)
- 6.Compute the clean image,$\widehat{X}={H}_{\mathit{\text{SDC}}}\xb7\mathrm{Y.}$
- 7.Reverse the homomorphic effect by taking the exponential of the $\widehat{X}$ as follows$\u0174=1{0}^{\widehat{X}}.$(20)
In essence, reversing the homomorphic effect in step 7 converts the logarithmic form of the filtered image to a linear form prior to image display.
Optimum value of the lagrange multiplier
The results in Figure 5 show that the SDC is not too sensitive to the selected value of the Lagrange multiplier. Notably, the results in Figure 5 show that for high noise level, (${v}_{n}^{2}>0.04$) the despeckle effect of the SDC, measured in terms of the SNR, shows improvement by 1 dB to 1.5 dB, as the Lagrange multiplier varies from 1 to 40. For lower value noise level, (${v}_{n}^{2}\le 0.04$) the SNR improvement is around 0.3 dB as the Lagrange multiplier varies from 1 to 10. In general, the results in Figure 5 show better SNR values for higher values of the Lagrange multiplier. However, it should be noted that high value of λ may results in oversmoothed images and cause loss of details. Consequently, the rule of selecting λ is that for noise variance less than 0.04, λ should be selected to be around 10 and with noise variance greater than 0.04 it should be selected to be less than 40.
Results and discussions
The value of 255 in Eq. (23) corresponds to the maximum possible pixel value and MSE is defined as in (22).
In the second part, the performance of the proposed SDC technique is investigated using a computer generated image and real US images. Here, the Lee filter is implemented with 7×7 window size, the homomorphic wavelet is used with Daubechies length-eight filter and a 7×7 window and the SBF technique is implemented according to the set up given in [19]. The SDC is implemented as in The subspace-based techniques for noise reduction section. The rank values and the noise variance of the different images are calculated using the method outlined in [31]. As for the Lagrange multiplier, the value is selected using the rule set in the previous section.
- 1.
Mean Preservation: A good speckle filter will maintains the mean intensity within a homogenous region.
- 2.Normalized Variance: The normalized variance indicates the performance of the filter in homogeneous areas. This metric is given by$\frac{\mathit{\text{var}}}{\mathit{\text{mea}}{n}^{2}}=\frac{\frac{1}{\mathit{\text{mn}}}\sum _{i=1}^{m}\sum _{j=1}^{n}{\left(X\left(i,j\right)-\stackrel{\u0304}{X}\right)}^{2}}{{\stackrel{\u0304}{X}}^{2}},$(24)
- 3.Autocorrelation: is another method of filter assessment in homogeneous area where close autocorrelation profile to the original image indicates better texture preservation. The autocorrelation for m×n image X is given as [36]$\rho (x,y)=\frac{\frac{1}{\left(m-\left|x\right|\right)\left(n-\left|y\right|\right)}\sum _{i}\sum _{j}X(i,j)X(i+x,j+y)}{\frac{1}{\mathit{\text{mn}}}\sum _{i=1}^{m}\sum _{j=1}^{n}X{(i,j)}^{2}},$(25)
- 4.Ultrasound Despeckling Assessment Index (USDSAI): is a modified Fisher discriminant contrast metric [37]. USDSAI gives an indication on how well a despeckling algorithm reduces variances in homogeneous classes while keeping the distinct classes well separated. The metric is defined as$\mathit{\text{USDSAI}}=\frac{\sum _{k\ne l}\left(\mathit{\text{mea}}{n}_{{C}_{k}}-\mathit{\text{mea}}{n}_{{C}_{l}}\right)}{\sum _{k=1}^{K}\mathit{\text{varianc}}{e}_{{C}_{k}}},$(26)
where |C _{ k }| denotes the number of pixels in class C _{ k }. If a despeckling filter produces classes that are well separated then the numerator in 26 will be large. Conversely, if the intraclass variance is reduced, then the denominator will be small giving large value of USDSAI indicating desirable image restoration and enhancement.
Evaluation of SDC performance in simulated speckle noise scenario
PSNR (in dB) values for despeckling of the test image in Figure 4
Noise variance | Noisy | Lee | Wavelet | SBF | SDC |
---|---|---|---|---|---|
0.02 | 20.61 | 19.88 | 21.66 | 21.68 | 21.73 |
0.04 | 18.98 | 19.73 | 20.56 | 20.49 | 20.60 |
0.06 | 16.80 | 19.46 | 18.18 | 19.05 | 19.84 |
0.08 | 14.61 | 18.96 | 15.61 | 18.23 | 19.11 |
0.10 | 11.69 | 18.07 | 12.26 | 17.81 | 17.67 |
Evaluation of SDC performance using a Field II simulated image
Normalized variance in denoised images of the cyst phantom in Figure 8
Original | Lee | Wavelet | SBF | SDC | |
---|---|---|---|---|---|
Region A | 0.03 | 0.02 | 0.02 | 0.02 | 0.01 |
Region B | 0.04 | 0.02 | 0.02 | 0.01 | 0.01 |
USDSAI value in denoised images of the cyst phantom in Figure 8
Original | Lee | Wavelet | SBF | SDC |
---|---|---|---|---|
1.00 | 2.10 | 1.80 | 3.07 | 3.00 |
Mean preservation in denoised images of the cyst phantom in Figure 8
Original | Lee | Wavelet | SBF | SDC | |
---|---|---|---|---|---|
Region A | 127.74 | 127.87 | 126.73 | 134.87 | 126.48 |
Region B | 125.60 | 125.69 | 123.80 | 133.02 | 125.17 |
Evaluation of SDC performance using real US images
In this experiment, the performance of the proposed SDC is analyzed and compared with Lee and Wavelet using ultrasound images captured from a patient as shown in Figure 2. The images are biopsy-verified studies and presented with non-palpable tumors initially detected by mammography [40]. These images are shown in Figure 2 for malignant and benign tumor. In Figure 2, the patient with malignant tumor was diagnosed with invasive ductal carcinoma whereas the patient with benign tumor was diagnosed with fibroadenoma. The image size is 1536×256 pixels with the x-axis and the y-axis giving lateral sizes and axial sizes of the image, respectively. The RF frames are recorded at 17 frame/second and a total of 12 seconds of data are acquired using a linear transducer array from the Antares^{®;} System. In order to obtain the B-mode ultrasound images, the URI Offline Processing Tools (URI-OPT) run on MATLAB platform is used to convert the RF data to the B-mode images as shown in Figure 2.
Normalized noise variance in the denoised images of real US images in Figure 2
Malignant tumor | Original | Lee | Wavelet | SBF | SDC |
---|---|---|---|---|---|
Region A | 0.012 | 0.003 | 0.001 | 0.003 | 0.003 |
Region B | 0.009 | 0.004 | 0.001 | 0.004 | 0.003 |
Benign tumor | Original | Lee | Wavelet | SBF | SDC |
Region A | 0.015 | 0.004 | 0.001 | 0.004 | 0.004 |
Region B | 0.018 | 0.007 | 0.003 | 0.007 | 0.005 |
Mean preservation in the denoised images of real US images in Figure 2
Malignant tumor | Original | Lee | Wavelet | SBF | SDC |
---|---|---|---|---|---|
Region A | 5.29 | 5.30 | 0.72 | 12.80 | 5.29 |
Region B | 7.49 | 7.49 | 0.87 | 14.90 | 7.46 |
Benign tumor | Original | Lee | Wavelet | SBF | SDC |
Region A | 4.83 | 4.84 | 0.68 | 12.32 | 4.83 |
Region B | 5.23 | 5.24 | 0.72 | 12.75 | 5.24 |
USDSAI value in denoised images of real US images in Figure 2
Original | Lee | Wavelet | SBF | SDC | |
---|---|---|---|---|---|
Malignant | 1.00 | 2.63 | 2.96 | 4.11 | 4.09 |
Benign | 1.00 | 2.83 | 2.70 | 4.22 | 4.17 |
Computational time (in second) of Lee, Wavelet, SBF and SDC for the US image in Figure 2
Lee | Wavelet | SBF | SDC | |
---|---|---|---|---|
Benign | 63.97 | 8.88 | 17.46 | 6.20 |
Malignant | 63.57 | 8.77 | 20.52 | 6.30 |
Conclusions
A subspace-based denoising technique for US images is presented and tested. The proposed technique, SDC is based on linear estimator and rank reduced subspace model to estimate the clean image from the corrupted one with speckle noise. The performance of the SDC is tested with simulated and real data, and compared with Lee and wavelet. The results indicate better noise variance reduction capability with the simulated images by the SDC than Lee, Wavelet and SBF in addition to less blurry effect. With the real case scenario, the SDC, Lee, Wavelet and SBF are tested with images obtained from raw RF data. The performances are calculated in terms of noise reduction, improvement in image contrast and preservation of the autocorrelation profiles. The results indicate that SDC offer better texture preservation, measured in terms of autocorrelation profiles and good contrast enhancement, measure in terms of USDSAI value. Finally, the computational complexity of the algorithms is compared and the results show that SDC required the least computational time compared to Lee, Wavelet and SBF.
Declarations
Acknowledgements
The authors would like to thank the Ultrasonic Imaging Laboratory at University of Illinois at Urbana-Champaign for providing validation data and the anonymous reviewers for their effort and constructive comments which helped in properly addressing the different issues and resulted in stronger proof of the proposed approach. This research work is funded under the Short-Term Internal Research Fund (STIRF) Grant Scheme (0153AA-C68), awarded by the Universiti Teknologi Petronas.
Authors’ Affiliations
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