Blind Source Parameters for Performance Evaluation of Despeckling Filters

The speckle noise is inherent to transthoracic echocardiographic images. A standard noise-free reference echocardiographic image does not exist. The evaluation of filters based on the traditional parameters such as peak signal-to-noise ratio, mean square error, and structural similarity index may not reflect the true filter performance on echocardiographic images. Therefore, the performance of despeckling can be evaluated using blind assessment metrics like the speckle suppression index, speckle suppression and mean preservation index (SMPI), and beta metric. The need for noise-free reference image is overcome using these three parameters. This paper presents a comprehensive analysis and evaluation of eleven types of despeckling filters for echocardiographic images in terms of blind and traditional performance parameters along with clinical validation. The noise is effectively suppressed using the logarithmic neighborhood shrinkage (NeighShrink) embedded with Stein's unbiased risk estimation (SURE). The SMPI is three times more effective compared to the wavelet based generalized likelihood estimation approach. The quantitative evaluation and clinical validation reveal that the filters such as the nonlocal mean, posterior sampling based Bayesian estimation, hybrid median, and probabilistic patch based filters are acceptable whereas median, anisotropic diffusion, fuzzy, and Ripplet nonlinear approximation filters have limited applications for echocardiographic images.


Introduction
Echocardiography is commonly used in the diagnosis of valvular regurgitation and stenosis. It is a noninvasive, safe, and a less expensive technique; but the low contrast, shadowing, and the speckle noise present make it hard for a clinician to read. The noise masks the finer clinical detail present in the image and thereby reduces the human visual ability for detecting the abnormalities. It reduces the potentiality of images in providing crucial and vital information [1]. The interpretation and clinical conclusions largely depend on the image quality and the experience of the cardiologist [1,2]. Hence, it is necessary to suppress speckle noise without altering the fine details from the transthoracic echocardiographic (TTE) images.
Filtering techniques based on the concepts such as wavelet [1,[3][4][5][6], anisotropic diffusion (AD) [1,4,5], a priori statistical information [1,4,7,8], multiresolution [9][10][11][12][13], nonlocal means (NLM) [4,14,15], total variation (TV) [16][17][18], bilateral [19,20], median [5][6][7], Wiener [5,13], geometric [1,5], local statistics [5], and fuzzy [21] filters have been advocated for noise reduction in ultrasound images. Various filtering techniques and performance parameters used by researchers are tabulated in Table 1. Most of the researchers have employed standard full-reference based metrics such as peak signal-to-noise ratio (PSNR), mean square error (MSE), structural similarity (SSIM) index, contrast-to-noise ratio (CNR), and root mean square error (RMSE), tabulated in Table 1, for evaluating the filter performance. These full-reference parameters evaluate the filter performance considering the output processed and the standard noise-free image. But, unfortunately, the noise-free reference image does not exist for echocardiographic images. Hence, these traditional parameters do not reflect the true performance in case of the echocardiographic images. The possible solution to this problem would be to use parameters such as speckle suppression index (SSI) [7,8], speckle suppression and mean preservation index (SMPI) [7,8], and beta metric ( ) [6,21]. These are blind source based parameters which do not need a standard noisefree reference image for estimating filter performance. The speckle noise present in echocardiographic images is multiplicative in nature. This noise masks the finer details necessary for abnormality diagnosis. Many filters result in image smoothing thereby suppressing the finer details. Hence, it would be necessary to know those of the filters which can suppress the noise while preserving the finer details.
Mateo and Fernández-Caballero [6] and Biradar et al. [21] employed beta metrics ( ) to evaluate edge preservation. Iqbal et al. [8] used SSI and SMPI to measure amount of speckle suppression and edge preservation index (EPI) for estimating edge preservation in synthetic aperture radar (SAR) images. This paper evaluates the performance of eleven types of filters based on SSI, SMPI, , figure of merit (FoM), and image quality index (IQI) and eleven other parameters along with the visual quality assessment and clinical validation. A list of filters types and their constituent approaches is tabulated in Table 2 for quick reference.

Despeckling Filters.
Loizou et al. [5,22] compared applications of 10 despeckling filters for suppression of speckle noise in US images of carotid artery. This paper studies the applications of despeckling filters (DsFs) considered by Loizou et al. [5,22] for TTE images. The despeckling filter based on the mean and the variance of the neighborhood is abbreviated as DsFlsmv where DsF stands for despeckling filter and ls, m, and v represent local statistics, mean, and variance, respectively. The output of first-order local statistics filter is given by where , is the local mean, denoised give the estimated denoised pixel values in the window, and , is the weighing factor [5,22], where ∈ [0, . . . , 1]. The weighing factor used in DsFlsmv filter is defined as where 2 is the variance of the moving window, 2 is the ratio between variance and mean computed on the whole image, and 2 = ∑ =1 2 / with 2 and as the variance and the mean of noise selected in the window [5,22]. The homogenous mask area filtering technique is abbreviated as DsFlsminsc filter (DsF-local statistics minimum speckle index). It works on the most homogeneous 5 × 5 neighborhood around each pixel using a subset of 3 × 3 window. The Wiener filter is based on the mean square error and it is abbreviated as DsFwiener [5,22]. The weight factor of DsFwiener filter is given by The filter based on the estimation of maximum homogeneity over a pixel neighborhood is called the DsFhomog filter. This filter estimates the homogeneous neighborhood around every pixel by taking into account pixels belonging to the processed neighborhood. The hybrid median is abbreviated as DsFhmedian (despeckling filter-hybrid median). It is an extension of DsFmedian (despeckling filter-median). The median values are calculated using three different windows, namely, normal shape, x-shape, and cross shape [5,22].

Fast Bilateral
Filter. The nonlinear characteristics of range filter in the bilateral filter increase the computational load. An improvement in the performance can be achieved using the raised cosine kernels. The generalized form of the filter based on the raised cosine kernel is given bŷ with ( ) = exp(− ( )), where is the coefficient of trigonometric function, is kernel degree, and ℎ ( ) = exp( ( )) and ( ) = ( )ℎ ( ) represent the auxiliary images and range kernel.
where are the wavelet shrinkage techniques [25][26][27][28][29]. During the implementation of wavelet shrinkage in the logarithmic domain, it is assumed that the noise variance is known, so that the focal point of discussion would be on the evaluation of the filter itself. The Bayes thresholding approach is a data driven subband adaptive wavelet shrinkage technique [25]. The concept of the multiscale product thresholding (MPT) is based on the idea that multiplications of the discrete wavelet transform (DWT) at adjacent scales enhance the edges and effectively suppress the noise [27]. In logarithmic probability shrinkage (ProbShrink) filtering method, the wavelet coefficients are multiplied with the estimated probability of the signal [21,30]. In SURELET [29], the pointwise thresholding is performed based on the minimization of SURE and LET. The interscale orthonormal wavelet thresholding (IOWT) is a parameterized denoising technique which alleviates the necessity of a statistical design model [26]. The limitations of block thresholding are overcome by incorporating SURE with NeighShrink resulting in NeighShrinkSURE (NSS) [28]. The details subbands are extracted and subband thresholding is reinforced with calculation of the optimal threshold and neighborhood size followed by thresholding using NeighShrink.

Multiresolution
Techniques. Some of the multiresolution based filtering techniques such as M-band ridgelet (MBR) [9,21], Ripplet nonlinear approximation (RNLA) [11,12], generalized likelihood estimation method (GLM) [1,4,13], and posterior sampling based Bayesian estimation (PSBE) [10] are considered in this paper for performance evaluation. The combination of M-band wavelet and ridgelet is known as M-band ridgelet (MBR). The texture is preserved using MBR filter [9,21]. In the GLM based filter, an initial classification of the coefficients is carried out based on the correlation among the prominent features across various resolution scales noniteratively. The initial classification is employed for the estimation of statistical distribution of the features of interest [1,4,13]. In the logarithmic PSBE, noise-free image details are estimated using Bayesian least square error calculations using conditional posterior sampling and then the average square error is minimized [10]. The generalization of curvelets known as Ripplet transforms is being achieved by incorporating support and degree parameters [11,12]. The Ripplet transformation in discrete domain is defined as where the Ripplet coefficients are represented by , ⃗ , [11,12].

Total Variation (TV) Based Filters. The TV based denois-
ing is based on the concept that the integral of absolute gradient of the noisy images would be high resulting in high total variation [18]. Let be a noisy image; the denoised image denoised can be obtained by minimizing the quadratic term with the TV regularization given by where the quadratic data term ∫ Ω ( − ) 2 fits in according to the least square fit, ∫ Ω |∇ | is the regularization term (denoising function), and is the weighting parameter which is the measure of smoothness. The fidelity term controls the amount of denoising by measuring local variance in the image in adaptive fidelity based TV (AFTV) [16]. Anisotropic TV (ATV) is based on split Bregman algorithm. The Bregman iterations are employed during the denoising process [17].

Anisotropic Diffusion (AD) Based Filters.
The AD is a nonlinear partial differential equation (PDE) based filtering technique that promotes diffusion in the homogeneous regions while holding back at edges [1,31]. In speckle reducing anisotropic diffusion (SRAD) filter, the diffusion function is controlled by instantaneous coefficient of variation (ICOV) [1,32]. The diffusion function employed in SRAD is of the form represented in where 0 stands for the "speckle scale function." The coherence enhancing diffusion (CED) employs structure tensor matrix for analyzing the local distribution of gradient vector [1,33]. Detail preserving anisotropic diffusion (DPAD) method estimates equivalence between threshold controlling the level of diffusion and variation in noise coefficient by incorporating modifications to the SRAD filter [4,34].
International Journal of Biomedical Imaging 5 2.10. Geometric Filter. The geometric filter works with an assumption that the images are made up of the valleys and the narrow walls. An intensity of pixel located at the center of a 3 × 3 window is compared with eight neighbors. Depending on the intensity values of the neighborhood pixels, the value is either incremented or decremented so that the values stand out in comparison with the intensity value in the neighborhood [1,35].
2.11. Nonlocal Mean Filter. The nonlocal means approach of denoising is governed by the patches around each pixel. The redundant information in the image is being used in optimized Bayesian nonlocal means (OBNLM) [4,14]. The patterns surrounding each pixel are compared instead of the intensity. In NLM based denoising, the Euclidean distance is computed between the patches. The generalization of this distance was advocated using probabilistic patch based (PPB) method [15]. The weight ( , ) in probabilistic patch based (PPB) filter between patch and patch with number of iterations is defined as where trade-off between noise suppression and fidelity estimation is achieved through parameters ℎ and ; , and , are the th pixel amplitude, where their previous values arê

Evaluation of Despeckling Filters
The despeckling filters are analyzed and evaluated for the clinical TTE images. These images are noisy; no noise-free reference image is available. Therefore, the evaluation of filters is carried out using the original speckled input. The analysis of performance is based on the blind assessment and the fullreference based image quality metrics. The blind assessment parameters such as the SSI [7,8], SMPI [7,8], and [6,21] are used in performance evaluation. These parameters assess the performance based on the original noisy image and the denoised images. The parameters such as the SSIM, IQI, and FoM [1,4,21] are used for measuring overall image quality, structure, and edge preservation. The traditional parameters such as PSNR, MSE, SNR, LMSE, RMSE, average difference, and maximum difference (MD) are also being computed using original TTE images. The traditional parameters may not reflect the true performance of the filters on real clinical images; therefore, the evaluation of performance is being validated by the practicing clinicians. All the experiments are implemented using MATLAB R2008a. The source codes provided by the authors of various papers are also being used with proper selection of parameters [5, 11, 13-17, 20, 25-30].

Clinical Echocardiographic Images.
The despeckling filters are applied to clinical database consisting of the TTE images of aortic valve and cardiac chambers. The database consists of images acquired in parasternal long axis (PLAX), parasternal short axis (PSAX), apical five-chamber (A5C), apical four-chamber (A4C), and apical two-chamber (A2C) views. The TTE image database was completely anonymized, with patient information provided. A total of 1000 images acquired from 20 patients in 5 views and 2 windows are used to evaluate and analyze the performance of despeckling filters.

Image Quality Metrics.
The parameters such as the SNR, PSNR, MSE, correlation coefficient ( ), RMSE, SC, LMSE, MD, Err3, Err4, NAE, NCC, and SSIM are computed using noisy and noise-free images [5,22]. Some of the performance parameters are defined below: where = + |Mean( den ) − Mean( org )|, = (max(Mean( den )) − min(Mean( den )))/Mean( org ), where is the scalar multiplier being utilized as penalization factor with typical value 1/9, den and ref are the number of pixels in original and processed images, respectively, is the Euclidean distance, Δ den and Δ org represent the filtered version of original and processed images, and pixel mean intensities in the region Δ den and Δ are represented by Δ den and Δ org , respectively [1, 6-8].

Results
The parameters being used in the implementation of filters are tabulated in Table 3. The results are being tabulated for each type of filter so that performance can be analyzed for intra-and interfilter type. The values of image quality metrics obtained on application of various filters are tabulated in Tables 4-6. The results for wavelet shrinkage and multiresolution techniques are tabulated in Table 4. The experimental results for despeckling, Fourier, and SAR filters are tabulated in Table 5.      SMPI values are superior by a factor of two compared to SAR filters. FoM is greater than one suggesting better denoising performance. Homomorphic Fourier filters result in smaller value of compared to Fourier filters. Fourier filters have ≥ 0.9 which speak of edge preservation. The issue of concern is smaller IQI using Fourier based techniques. It is observed that IQI is less than 0.4 using the FIF and FBF filters. The SAR filters oversmooth the texture present in the TTE images. The values of SSI are greater than one using Lee, Kaun et al., and Frost et al. 's filters indicating that speckle noise is not suppressed. The performance of SAR filters is poor in terms of SMPI. The major problems using SAR filters are high values of SMPI and SSI. The fuzzy filters perform well in terms of IQI, FoM, and SSI with fractionally higher SMPI (≤4) but have poor beta metric. The GW filter results in the least SSI value among all the fuzzy and hybrid fuzzy filters. The hybrid fuzzy filters have smaller SMPI compared to logarithmic fuzzy filters. All fuzzy and hybrid fuzzy filters have FoM greater than 0.8. The modified geometric filter preserves the edges as exhibited by ≥ 0.9.

Total Variation, Diffusion, and Nonlocal Mean Based Filters.
The performance of TV based filters is moderate in terms of IQI and SMPI. The AFTV and ATV filters result in poor IQI (≤0.3) and moderate , FoM, and SMPI. These filters have SSI <1. All the TV filters have FoM greater than 0.8 except for the AFTV filter. Filters such as AFTV and TV have ≤ 0.5. The output images on application of PPB and NLM filters result in SSI ≤1. The DPAD, FBL, NLM, and PPB filters have SMPI far less compared to SAR filters proving their superior speckle suppression capabilities. The FoM using the DPAD and PPB filters is almost equal to one and is far superior compared to the SAR and OBNLM filters. The IQI is comparatively less using the PPB (0.4), NLM (0.6), and DPAD (0.6) filters whereas FBL (0.7) is fractionally higher.
The performances in terms of IQI, , FoM, SMPI, SSI, and MD for 1000 TTE images are tabulated in Table 7. The performances of the filters are also evaluated in terms of traditional parameters and the values are tabulated in Table 8. The results are being represented in the form of average plus/minus standard deviation. The DsFwiener, DsFsard, GLM, PPB, GWF, DPAD, and PSBE stand out among the others in Table 8. Clinical Validation. The clinical validation of preprocessed images is carried out by seeking opinion of four practicing cardiologists at PGI, Chandigarh. One of the authors of this paper is a senior practicing cardiologist, who initially graded the quality of the processed images. The grading of images is based on visual perception of the practicing clinicians. The procedure of grading consisted of awarding a grade value in the range of 1 to 10 where 1 signifies the poor quality of processed image and grade 10 is assigned to the best visual  quality image. The analyses of these grades reveal that the filters such as the DsFgf4d, DsFhomog, DsFlsmv, DsFhmedian, DPAD, GLM, PSBE, NLM, and PPB are acceptable whereas DsFhomo, DsFmedian, DsFad, TMED, HTMED, and RNLA filtered images are clinically not suitable.

Conclusion
The despeckling applications of eleven types of filters are analyzed in this paper in terms of blind and full-reference parameters. The traditional parameters often fail to reflect the true performance of the filters in the absence of a noise-free reference image. The parameters such as speckle suppression index, speckle suppression and mean preservation index, and beta metric are used to study the speckle suppression and edge preservation capability of each filter. The image quality and structural preservation are analyzed using SMPI, FoM, IQI, and SSI. Various types of benchmark filters are available and it would be very difficult to choose the best clinically acceptable filter. It is also necessary to remove speckle noise but with the edges preserved. The major contributions of this paper are as follows: it helps in selecting the best filters suitable for clinical TTE images among eleven types of filters and their constituents, it studies and evaluates the performance in terms of blind and full-reference based parameters, and evaluations of filters based image quality metrics are validated by practicing clinicians. Based on the quantitative evaluation and clinical validation, it is concluded that the performances of DsFgf4d, DsFhomog, DsFlsmv, DsFhmedian, DPAD, GLM, PSBE, NLM, and PPB filters are acceptable.

Ethical Approval
All procedures followed were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and with Helsinki Declaration of 1975, as revised in 2000(5).

Consent
Informed consent was obtained from all patients for being included in the study.