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5 Real-Time Speckle and Impulsive Noise Suppression in 3-D Ultrasound Imaging Francisco J. Gallegos-Funes, Jose M. de-la-Rosa-Vazquez, Alberto J. Rosales-Silva and Suren Stolik Isakina National Polytechnic Institute of Mexico Mexico 1. Introduction Ultrasound imaging is considered one of the most powerful techniques for medical diagnosis and is often preferred over other medical imaging modalities because of noninvasive, portable, versatile and low-cost properties (Webb, 2002; Abd-Elmoniem, 2002; Porter, 2001; Shekhar, 2002). A fundamental problem in the field of ultrasound imaging is the speckle noise influence, which is a major limitation on image quality in ultrasound imaging. Imaging speckle is a phenomenon that occurs when a coherent source and a noncoherent detector are used to interrogate a medium, which is rough on the scale of the wavelength. Speckle noise occurs especially in images of the liver and kidney whose underlying structures are too small to be resolved using long ultrasound wavelength. The presence of speckle noise affects the human interpretation of the images as well the accuracy of computer-assisted diagnostic techniques (Nikolaidis, 2000; Kim & Park, 2001) The goal of this chapter is the capability and real-time processing features of the robust MML (Median M-type L) filters to remove speckle and impulsive noise in 3-D ultrasound images (Gallegos-Funes et al., 2008, Varela-Benitez et al., 2007). The Texas Instruments DSP TMS320C6711 is used to implement the algorithms (Texas Instruments, 1998; Kehtarnavaz, 2001). Based on the processing time values of each a 3-D filter, different configurations of sweeping cubes (voxels) are used to obtain a balance between the processing time and quality of the restoration of 3-D images (Nikolaidis, 2000). The criteria used to measure the performance of filters are: the peak signal-to-noise ratio (PSNR) to characterize the noise suppression, and the mean absolute error (MAE) to evaluate the preservation of edges and fine details (Bovik, 2000; Astola & Kuosmanen, 1997; Kotropoulos & Pitas, 2001; Pitas & Venetsanopoulos, 1990). Extensive simulation results have demonstrated that the proposed filters can consistently outperform other filters used as comparative by balancing the tradeoff between noise suppression, detail preservation, and processing time. 2. Problem formulation All coherent imaging that include laser, SAR, and ultrasound imagery are affected by speckle noise (Abd-Elmoniem, 2002; Bovik, 2000; Kotropoulos & Pitas, 2001). Speckle may appear distinct in different imaging systems but it is always manifested in granular pattern due to image formation under coherent waves. A general model for ultrasound speckle noise can be written as (Abd-Elmoniem, 2002), www.intechopen.com 82 x ( i , j ) = S ( i , j )ηm ( i , j ) + η a ( i , j ) Ultrasound Imaging (1) where x ( i , j ) is a noisy observation (i.e., the recorded ultrasound image) of the twodimensional (2-D) function S ( i , j ) (i.e., the noise-free image that has to be recovered), ηm ( i , j ) and η a ( i , j ) are the corrupting multiplicative and additive speckle noise components, respectively, and i and j are variables of spatial locations that belong to 2-D space of all real numbers ( i , j ) ∈ ℜ2 . Generally, the effect of the additive component (such as sensor noise) of the speckle in ultrasound images is less significant than the effect of the multiplicative component (coherent interference). Thus, ignoring the term η a ( i , j ) , can be rewritten (1) as (Abd-Elmoniem, 2002), x ( i , j ) = S ( i , j )ηm ( i , j ) . (2) To transform the multiplicative noise model into the additive noise model, we apply the logarithmic function on both sides of (2) or log x ( i , j ) = log S ( i , j ) + log ηm ( i , j ) , (3) x l ( i , j ) = S l ( i , j )ηml ( i , j ) , (4) x ( i , j ) = ηi ( S ( i , j )ηm ( i , j ) ) (5) where ηml ( x , y ) is approximated as additive white noise. We assume here that the speckle pattern has a white Gaussian noise model. Therefore, the acquisition or transmission of digitized images through sensor or digital communication link is often interfered by impulsive noise (Astola & Kuosmanen, 1997; Pitas & Venetsanopoulos, 1990). Thus, the impulsive noise is added to the model (2) as follows (Astola & Kuosmanen, 1997) ⎧⎪random valued spike with probability P . where ηi ( f ( i , j ) ) is the functional ηi ( f ( i , j ) ) = ⎨ ⎪⎩ f ( i , j ) otherwise 3. 3-D Median M-type L-filters Consider the monochromatic 3-D image x(i , j , k ) where i and j are the 2-D spatial axes and k is the time axis or may be the third dimension for 3-D images (Nikolaidis & Pitas, 2000; Kim & Park, 2001). When the current pixel location is (i , j , k ) , a 11-point window W (i , j , k ) , is defined as follows (Kim & Park, 2001): W (i , j , k ) = {x ( i − 1, j − 1, k ) , x ( i , j − 1, k ) , x ( i + 1, j − 1, k ) , x ( i − 1, j , k ) , x ( i , j , k ) , x ( i + 1, j , k ) , x ( i − 1, j + 1, k ) , x ( i , j + 1, k ) , x ( i + 1, j + 1, k ) , x ( i , j , k + 1 ) , x ( i , j , k − 1 )} (6) From eq. (6), the window W (i , j , k ) includes a 3x3 window centered at the current pixel of the current frame and the current pixel’s corresponding pixels in the previous and the next frames, as shown in Figure 1. www.intechopen.com 83 Real-Time Speckle and Impulsive Noise Suppression in 3-D Ultrasound Imaging Next Frame x(i,j,k+1) Current Frame x(i,j,k) k Previous Frame j x(i,j,k-1) i A 3-D image can be considered as a 3-D matrix x [ i ][ j ][ k ] or x(i , j , k ) of dimensions N 1 × N 2 × N 3 where i , j , k denote row, column, and slice (image) coordinates, respectively (Nikolaidis & Pitas, 2000). The 3-D representation is depicted in Figure 2. Each a voxel (volume elements) has physical size di × dj × dk physical units (e.g. mm3 or μ m3 ). Recently (Gallegos & Ponomaryov, 2004; Gallegos et al., 2005), we proposed the combined RM (Rank M-type) –estimators for applications in image noise suppression. These estimators use the M-estimator combined with the R-estimator, such as the median or ABST (Ansari-Bradley-Siegel-Tukey) estimator. It was demonstrated that the robust properties of the RM-estimators exceed the robust properties of the base R- and M- estimators for the impulsive and speckle noise suppression (Gallegos & Ponomaryov, 2004). The RM-estimator used in the proposed 3-D filtering scheme is presented in such a form (Gallegos & Ponomaryov, 2004; Gallegos et al., 2005): Fig. 1. The elements of the 11-point window W (i , j , k ) . { ( { }) θ medM = MED X pψ X p − MED X , p=1,… , N } (7) where θ medM is the Median M-type (MM) estimator, X p are data samples, p = 1,… , N , ψ is the normalized function ψ : ψ ( X ) = Xψ ( X ) , and X is the primary data sample. The MM-L type filter has been designed using the MM-estimator to increase the robustness of the L-filter. The detail description of such a filtering scheme is presented in recent works (Gallegos-Funes et al., 2008; Varela-Benitez et al., 2007), and in here we propose its modifications for 3-D imaging applications. So, the 3-D MM-L (Median M-type L) filter is defined as follows: f RM -L ( i , j , k ) = www.intechopen.com { ( { }) } med a p ⎡⎢ X p ⋅ ψ X p − med X ⎤⎥ ⎣ ⎦ , amed (8) 84 Ultrasound Imaging k k slice i dk dj j ( di { }) Fig. 2. 3-D representation as a 3-D array. where X p ⋅ ψ X p − med X represent the selected pixels in accordance with the influence function into a rectangular 3-D grid of voxels, ap = ∫pp−n1 n h ( λ ) dλ ∫01 h ( λ ) dλ are the weighted ap , the filtering 3-D grid size is N 1 × N 2 × N 3 , N p = ( 2 L + 1 ) and lp , mp , np = −L ,… , L , and coefficients where h(λ) is a probability density function, amed is the median of coefficients 2 X p is the input data sample from the x(i , j , k ) of the 3-D image contaminated by noise in the rectangular 3-D grid where i and j are the 2-D spatial axes and k is the time axis (or third dimension). We use in the proposed 3-D filter the Tukey biweight influence function defined as (Hampel et al., 1986; Huber, 1981), ( ) ⎧⎪X 2 r 2 - X 2 , X ≤ r ψ bi( r ) ( X ) = ⎨ ⎪⎩ where r is connected with the range of ψ ( X ) . 0, X > r (9) To improve the properties of impulsive noise suppression of the proposed MM L-filter we introduced an impulsive detector, this detector chooses if that voxel is filtered. The impulsive detector used here is defined as (Aizenberg et al., 2003): ( ( ) ) ( ( ) ) ( ) ⎡ rank X ≤ T ∨ rank X ≥ N − T ⎤ ∧ X − MED X ≥ T , ijk 1 ijk p 1 ⎥ ijk 2 ⎣⎢ ⎦ (10) where Xijk is the central voxel in the 3-D grid, T1>0 and T2≥0 are thresholds. We noted that the weighted coefficients of proposed 3-D filter are calculated using the exponential, Laplacian, and Uniform distribution functions (Pitas & Venetsanopoulos, 1990; Hampel et al., 1986) by each sliding filter window because the influence function selects www.intechopen.com 85 Real-Time Speckle and Impulsive Noise Suppression in 3-D Ultrasound Imaging which pixels are used and then compute the weighted coefficients of L-filter according with the number of pixels used into the filtering window. The parameters of the 3-D MM L-filters were found after numerous simulations by means of 2 use a 3x3x3 grid (i.e., N 1 × N 2 × N 3 = 27 , l , m , n = −1,… ,1 , and N p = ( 2L + 1 ) = 9 ). The idea was to find the parameters values when the criteria PSNR and MAE should be optimum. The optimal parameters of proposed filters are: T1=3 and T2=15 for the impulsive detector, and r=15 for Tukey influence function. Processing times may change when we use other values for the parameters, increasing or decreasing processing times. The PSNR and MAE values change within the range of ±(510)%, it is due to the proposed fixed parameters that can realize the real-time implementation of the 3-D MM L-filters. 4. Experimental results The objective criteria employed to compare the performance of noise suppression of different filters was the peak signal to noise ratio (PSNR) and for the evaluation of fine detail preservation the mean absolute error (MAE) (Bovik, 2000; Pitas & Venetsanopoulos, 1990): ⎡ ( 255 )2 ⎤ ⎥ , dB PSNR = 10 ⋅ log ⎢ ⎢⎣ MSE ⎥⎦ MAE = (11) N1 -1 N2 −1 N3 −1 1 ∑ ∑ ∑ S(i , j , k ) − fˆ (i , j , k ) N 1N 2 N 3 i = 0 j = 0 k = 0 (12) N1 − 1 N 2 −1 N3 −1 2 1 ∑ ∑ ∑ ⎡⎣S(i , j , k ) − fˆ ( i , j , k )⎤⎦ is the mean square error, S ( i , j , k ) is N 1N 2 N 3 i = 0 j = 0 k = 0 the original free noise 3-D image, fˆ ( i , j , k ) is the restored 3-D image, and N , N , N are the where MSE = 1 2 3 sizes of the 3-D image. The runtime analysis of the 3-D MM L-filters and other concerned filters used as comparative were implemented by using the Texas Instruments DSP TMS320C6711 (Texas Instruments, 1998). This DSP has a performance of up to 900 MFLOPS at a clock rate of 150 MHz. The filtering algorithms were implemented in C language using the BORLANDC 3.1 for all routines, data structure processing and low level I/O operations. Then, we compiled and executed these programs in the DSP TMS320C6711 applying the Code Composer Studio 2.0. The processing time in seconds includes the time for acquisition, processing, and storing data. The described 3-D MM L-filters with Tukey biweight influence function and different distribution functions have been evaluated, and their performance has been compared with different nonlinear 2-D filters which were adapted to 3-D. The filters used as comparative were the modified α-Trimmed Mean (Astola & Kuosmanen, 1997; Bednar & Watt, 1984), Ranked-Order (RO) (Astola & Kuosmanen, 1997; Pitas & Venetsanopoulos, 1990), Multistage Median (MSM1 to MSM6) (Arce, 1991), Comparison and Selection (CS) (Astola & Kuosmanen, 1997; Pitas & Venetsanopoulos, 1990), MaxMed (Nieminen & Neuvo, 1988), Selection Average (SelAve) (Astola & Kuosmanen, 1997; Pitas & Venetsanopoulos, 1990), Selection Median (SelMed) (Astola & Kuosmanen, 1997; Pitas & Venetsanopoulos, 1990), Lower-Upper-Middle (LUM, LUM Sharp, and LUM Smooth) (Hardie & Boncelet, 1993), and Rank M-type K-nearest www.intechopen.com 86 Ultrasound Imaging Neigbour (RM-KNN) (Ponomaryov et al., 2006) filters. These filters were computed according to their references and were adapted to 3-D imaging. Several experiments were realized to investigate the performances of the different techniques in 3-D imaging (VarelaBenitez et al., 2007). 4.1 Experiment 1 Figure 3 shows the 3-D space used to reconstruct the human organ as an object into 3-D space with its real measures. The coordinate z represents each a 2-D image of the sweeping in the 3-D space, and the coordinates x and y represent the height and width of the 2-D image, respectively. Having the 3-D image, one can carry out courts in the different plane yz, xy, and xz. z x d = 0.63 mm y Fig. 3. 3-D ultrasound image representation. The experiment 1 was realized by degraded an ultrasound sequence of 640x480 pixels with 90 frames (3-D image of 640x480x90 voxels) with 5 and 20% of impulsive noise and with the natural speckle noise of the 3-D image. Table 1 presents the performance results of proposed filters and the comparative results of different non linear filters applied to a frame of the original sequence. From Table 1 we observe that when the noise corruption is 5%, the proposed filters almost have the same performances that other filters in terms of noise suppression and detail preservation, but when the noise corruption is high the best results are given by the MM-KNN filters. It can be seen from Table 1 that the processing time for proposed filters is less in comparison with the MM-KNN filters but the times of proposed ones are large in comparison with other filters. It is easy to see that the processing time values for MM L-filters are decreased but the performance criteria PSNR and MAE are sufficiently acceptable (see Table 1) in comparison with other RM filters such as the RM-KNN (Median, Wilcoxon, and ABST –KNN) filters and other filters proposed as comparative. www.intechopen.com 87 Real-Time Speckle and Impulsive Noise Suppression in 3-D Ultrasound Imaging Impulsive noise percentage 5% 3-D Filters LUM Smooth LUM Sharp LUM MaxMed Modified Trimmed Mean MSM1 MSM2 MSM3 MSM4 MSM5 MSM6 SelAve SelMed RO MM-KNN Cut MM-KNN Hampel WM-KNN Hampel ABSTM-KNN Hampel MM-L TUKEY Uniform MM-L TUKEY Laplacian MM-L TUKEY 20% PSNR MAE Time PSNR MAE Time 29.94 17.36 18.53 27.10 24.90 28.92 28.13 27.46 27.94 29.44 28.29 26.83 27.43 26.50 28.83 28.79 22.75 27.45 28.30 28.03 27.52 2.75 17.28 15.51 6.24 7.04 4.25 5.06 5.94 5.33 3.77 5.06 6.97 5.63 6.67 4.27 4.31 10.91 5.21 4.77 5.00 5.63 4.122 4.224 4.317 1.1981 2.1716 0.5846 0.5773 1.2681 1.2367 1.2198 1.1667 1.9620 2.3240 1.6836 20.49 20.51 38.54 34.14 3.7731 3.7733 3.7732 25.26 15.90 17.59 23.24 24.71 26.68 26.18 26.88 27.13 25.98 27.67 22.34 26.31 26.27 27.91 27.89 21.98 26.77 25.93 25.80 24.84 4.87 20.17 17.68 9.20 7.35 5.30 6.00 6.46 5.81 5.17 5.45 14.33 6.37 6.94 5.14 5.16 11.59 6.00 5.69 5.83 7.01 5.754 5.867 5.984 1.1981 2.1716 0.5846 0.5773 1.2681 1.2367 1.2198 1.1667 1.9620 2.3240 1.6836 20.63 21.26 45.06 38.00 3.7732 3.7733 3.7737 Table 1. Performance results of different filters in a frame of ultrasound sequence degraded with impulsive noise. Figure 4 displays the visual results in terms of restored images obtained by the use of different filters according to Table 1 by means of use the xz plane. In Figure 4, we can see that the proposed MM L-filters provide good results in noise suppression and detail preservation. 4.2 Experiment 2 The experiment 2 was performed in the same sequence but it was degraded with 0.05 and 0.1 of variance of speckle noise added to the natural speckle noise of the sequence. The performance results are depicted in Table 2 by use of a frame in the xy plane of the sequence. From Table 2 we observe that the 3-D MM L-filters provide the best results in comparison to other comparative filters proposed. Figure 5 exhibits the visual results of restored images obtained by use of different filters according to Table 2, we observe that the proposed filters provide the best results in speckle noise suppression and detail preservation in comparison with other filters used. www.intechopen.com 88 Ultrasound Imaging a) b) c) d) e) f) Fig. 4. Visual results in a frame of ultrasound sequence. a) original frame, b) frame degraded by 20% of impulsive noise, c) restored frame by MSM5 filter, d) restored frame by MM-KNN (Hampel) filter, e) restored frame by MM L-filter (Exponential), f) restored frame by MM Lfilter (Laplacian). www.intechopen.com 89 Real-Time Speckle and Impulsive Noise Suppression in 3-D Ultrasound Imaging Speckle noise variance 3-D Filters 0.05 0.1 PSNR MAE PSNR MAE CS 15.44 32.88 13.84 39.78 LUM Smooth 17.92 25.14 15.44 33.82 LUM Sharp 15.63 30.93 14.44 36.43 LUM 15.52 31.43 14.38 36.75 MaxMed 18.56 24.21 15.92 32.91 Modified α-Trimmed Mean 20.42 15.12 19.10 18.66 MSM1 20.57 17.62 18.06 23.68 MSM2 20.48 17.79 18.04 23.73 MSM3 22.42 14.21 20.26 18.46 MSM4 21.70 15.40 19.35 20.35 MSM5 19.55 20.21 16.96 27.44 MSM6 22.08 14.69 19.74 19.37 SelAve 21.18 17.65 19.19 22.81 SelMed 20.84 15.75 19.01 20.09 RO 21.59 14.520 19.80 18.18 MM-KNN Hampel 21.57 15.169 19.04 20.80 MM-L TUKEY Uniform 29.88 5.016 28.618 5.743 MM-L TUKEY Laplacian 28.80 5.646 28.19 6.020 MM-L TUKEY Exponential 28.03 6.261 26.30 7.666 Table 2. Performance results of different filters in a frame of ultrasound sequence degraded with speckle noise. www.intechopen.com 90 Ultrasound Imaging a) b) c) d) e) f) Fig. 5. Visual results in a frame of ultrasound sequence. a) Original frame, b) frame degraded by 0.05 of variance of speckle noise, c) restored frame by MSM6 filter, d) restored frame by MM-KNN filter, e) restored frame by MM L-filter (Uniform), f) restored frame by MM-L filter (Laplacian). 4.3 Experiment 3 Experiment 3 is related to different voxels cube configurations to provide better noise reduction. Figure 6 shows nine configurations of voxels used in the proposed 3-D filtering algorithms. It is obvious that by using less voxels in the different cube configurations the processing time can be decreased. In this experiment the ultrasound sequence was degraded www.intechopen.com