35
CHAPTER 2
HYBRID MEDIAN FILTER IN DESPECKLING OF ULTRASOUND
IMAGES
Spatial domain filtering is one of the most widely used techniques in
image processing for image enhancement, and it operates on the pixels
directly. The spatial domain filters convolve a mask with the image, and these
filters can be categorized as linear and nonlinear filters. The main drawbacks
of these filters are that, they remove lines, round off corners and blur edges.
These are the inevitable features for applications such as medical imaging and
remote sensing. To overcome these drawbacks, a corner preserving median
filter also called as Hybrid Median Filter (HMF) was proposed (Davies 2006)
in general image processing applications.
In this chapter two speckle reduction schemes are proposed based
on HMF. The first approach is a Modified HMF (MHMF) and the second
approach is Adaptive Window HMF (AWHMF).
2.1 HYBRID MEDIAN FILTER
The HMF is a three-step ranking operation. In a 5x5 pixel
neighbourhood, pixels can be formed into two sub-neighbourhoods consisting
of 45o neighbours and 90o neighbours as shown in Figure 2.1. The pixels in
these two neighbourhoods are ranked separately and the median value from
each group is computed. The filter compares these two median values with
the centre pixel and calculates the median value. Finally the centre pixel is
replaced with the median value computed in the last step.
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(a) 5 5 neighbourhood (b) 45o neighbours (c) 90o neighbours
Figure 2.1 Neighbourhood pixels used in HMF
2.1.1 HMF Algorithm
The steps of the HMF are as follows:
Step1: A window of size 5x5 is selected and two sub- neighbourhoods
(45o neighbours), and (90o neighbours) are formed.
Step2: The pixels in the two sub - neighbourhoods are arranged in
ascending order and the median value of each group is computed.
Step3: The two median values obtained in step 2 and the centre pixel are
compared and the median of the three values is computed.
Step4: Finally the centre pixel is replaced by the median value computed in
step 3.
The computational complexity is less in the three step ranking
operation when compared to the median filter. In each step, the ranking
operations take place only for a smaller number of values than used in a
square region of the same size. The main advantage of this filter is that, it
does not eliminate lines and preserves edges better than the traditional mean
and median filters.
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In this work two approaches have been proposed to improve the
edge preservation capability of the filter and to make the HMF suitable for
ultrasound image denoising.
2.2 MODIFIED HYBRID MEDIAN FILTER
A Modified Hybrid Median Filter (MHMF) is developed for speckle
reduction and edge preservation of ultrasound images. It works on the sub-
windows similar to HMF. The window size used for the proposed filter is
5x5. The pixels in 45o neighbours and 90o neighbours are represented by
and respectively. To preserve the diagonal edges, the maximum value of
the pixels in sub-neighbourhood is taken, instead of median as in HMF
and is illustrated in Figure 2.2.
The MHMF is implemented as follows:
Let W be a square filter window, and the
pixels in this window are divided into four sub-windows consisting of the
pixels in horizontal ( , vertical and diagonal ( and
directions, and are given by Equation (2.1) to Equation (2.4).
(2.1)
(2.2)
(2.3)
(2.4)
The window is a combination of the two sub-
windows , and the centre pixel and is given in Equation (2.5).
38
Similarly the two sub-windows and the centre pixel are combined to
represent the pixels in as in Equation (2.6).
(2.5)
(2.6)
The output of the MHMF is represented using Equation (2.7).
(2.7)
Figure 2.2 Modified Hybrid Median Filter
"+" sub-neighbourhood
Maximum value from sub-neighbourhood
First stage Ranking
Original pixel
Original pixel and Neighbours
"x" sub-neighbourhood
Second stage Ranking
Median value from sub-neighbourhood
New pixel value
39
2.2.1 MHMF Algorithm
The steps followed in the MHMF algorithm are given below:
Step1: A window of size 5x5 is selected and two sub - neighbourhoods
and are formed.
Step 2: The pixels in the sub-neighbourhoods and are arranged in
ascending order.
Step 3: Median value of the pixels in and maximum value of the pixels
in are computed.
Step 4: The values obtained from step 3 and the centre pixel are arranged in
ascending order and the median value is obtained.
Step 5: Finally the filter replaces the centre pixel with the median value
obtained in step 4.
2.3 ADAPTIVE WINDOW HYBRID MEDIAN FILTER
The major limitation of the spatial domain speckle reduction filters
is that, they are sensitive to the shape and size of the window (Loizou &
Pattichis, 2008). If a larger window size is used, the filter will be more
effective at reducing noise but will also blur edges; whereas a smaller sized
window decreases the noise reduction ability, thus making the filter
inefficient.
In this work the window size of the hybrid median filter is made
adaptive for effective speckle reduction and edge preservation.
In the proposed adaptive window hybrid median filter, the size of
the window used for filtering the noisy image is selected based on the image
40
region. Since the correlation among the pixels is high in the homogeneous
regions, a window of size 5x5 is used, and as the non homogeneous regions
have less number of correlated pixels in its neighbourhood a smaller window
of size 3x3 is used in these areas. To distinguish smooth and edge regions,
edge detection operators are used. In the literature, many edge detection
operators are proposed such as Prewitt, Roberts, Sobel and Canny (Canny
1986, Maini & Aggarwal 2009). The Sobel operator is used in the proposed
algorithm, since it is less sensitive to isolated high intensity point variations. It
also gives an estimate of edge direction as well as edge magnitude at a point
which is more informative. The hardware implementation of this operator is
also relatively easier. The edge detected image is obtained by thresholding the
gradient image computed using Sobel masks. As the edges are treated
separately the edge preservation ability of the proposed algorithm is good.
The algorithm for AWHMF is given below:
2.3.1 AWHMF Algorithm
Step1: The Sobel operator is applied on the noisy image.
Step2: The edge image is obtained by thresholding the gradient image
computed using Sobel masks. The pixels belonging to smooth and
operation is shown in Figure 2.3.
Step 3: Adaptive window hybrid median filter is applied on the noisy
image. The size of the window is varied with the following
concepts.
(i) If the pixel to be processed is identified as an edge pixel then
the size of the window is 3x3.
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(ii) Else if the pixel belongs to smooth region, the size of the
window is 5x5.
Step 4: All the filtered pixels p1 and q1corresponding to p and q are
combined to obtain the denoised image as shown Figure 2.4.
Figure 2.3 Edge image extraction using Sobel operator
Figure 2.4 Filtering operation of AWHMF
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2.4 SIMULATION RESULTS AND DISCUSSIONS
The simulation is carried out in MATLAB environment to assess the
performance of the proposed filters MHMF and AWHMF. For quantitative
MATLAB. The variance ( n2) of the speckle noise is varied from 0.02 to
0.07. In this work the performance of the proposed method is compared
against the performance of the existing algorithms like median (Nixon &
Aguado 2002), Lee (Lee 1980), Kuan (Kuan et al 1985), Frost (Frost et al
1982), HMF (Davies 2006) and NCD (Abd-Elmoniem et al 2002) for
different noise variances.
The Peak Signal to Noise Ratio (PSNR), Root Mean Squared Error
(RMSE), Edge Preservation Index (EPI), Correlation Coefficient (CoC),
Feature Similarity (FSIM) Index and Execution Time (ET) are used as
performance measures.
Test Image 1: The performance of the proposed algorithm is tested using
synthetic image (Test image1) of size 128 x 128, which consists of regions
with uniform intensity and sharp edges, and is compared against the existing
denoising algorithms for the speckle noise of variance ranging from 0.02 to
0.07.
The PSNR values of various algorithms are listed in Table 2.1. The
largest PSNR value for a particular variance of speckle noise is highlighted to
show the best performance. From this table, it can be observed that for the
lowest noise variance of 0.02 the performance of MHMF is better than the
standard speckle reduction filters Lee, Kuan, Frost and the median. The
AWHMF algorithm gives 1dB PSNR better than the existing algorithms for
speckle noise of variance ranging from 0.02 to 0.05 and above 0.05 it
performs more or less similar to the existing filters.
43
Table 2.1 PSNR values obtained for Test Image 1
Peak Signal to Noise Ratio (PSNR) in dB
Filters Noise variance
0.02 0.03 0.04 0.05 0.06 0.07
Speckled image 28.93 27.21 25.97 25.09 24.20 23.51
Median(3x3) 29.90 29.28 28.61 28.16 27.51 27.18
Median(5x5) 27.97 27.43 27.18 26.82 26.42 26.01
HMF(3x3) 31.44 29.70 28.62 27.50 26.96 26.21
HMF(5x5) 31.17 29.84 28.79 28.17 27.54 27.02
Lee 29.86 29.51 29.13 28.85 28.73 28.30
Kuan 29.90 29.47 29.10 28.87 28.69 28.35
Frost 30.62 29.77 29.04 28.69 28.10 27.52
NCD 31.98 29.51 27.63 26.43 25.51 24.65
MHMF 30.85 29.11 27.96 26.97 26.50 26.13
AWHMF 32.59 31.05 30.09 29.07 28.42 27.73
The proposed algorithms are also tested with the Root Mean Square
Error (RMSE), which is the square root of the squared error averaged over the
M x N (size of the image) array. The RMSE values of the MHMF, AWHMF
and existing algorithms for synthetic image are given in Table 2.2. The
smallest (best) RMSE value for a particular noise variance of speckle noise is
highlighted for analysis purpose. From the table it is evident that the RMSE
value of AWHMF is smaller for noise variance from 0.02-0.05 and above
0.05 the performance of standard speckle filters Lee and Kuan is better when
compared to the other filters.
44
Table 2.2 RMSE values obtained for Test Image 1
Root Mean Square Error (RMSE)
Filters Noise variance
0.02 0.03 0.04 0.05 0.06 0.07 Speckled image 0.0506 0.0617 0.0711 0.0787 0.0872 0.0944 Median(3x3) 0.0452 0.0486 0.0525 0.0553 0.0596 0.0619 Median(5x5) 0.0575 0.0594 0.0634 0.0650 0.0672 0.0742 HMF(3x3) 0.0379 0.0463 0.0524 0.0597 0.0635 0.0692 HMF(5x5) 0.0391 0.0455 0.0514 0.0552 0.0594 0.0630 Lee 0.0455 0.0473 0.0495 0.0511 0.0518 0.0544 Kuan 0.0453 0.0475 0.0496 0.0509 0.0520 0.0541 Frost 0.0416 0.0459 0.0499 0.0520 0.0556 0.0581 NCD 0.0356 0.0473 0.0587 0.0675 0.0750 0.0828 MHMF 0.0406 0.0496 0.0569 0.0631 0.0663 0.0721 AWHMF 0.0332 0.0396 0.0443 0.0498 0.0537 0.0571
Table 2.3 EPI values obtained for Test image 1
Edge Preservation Index (EPI) Filters Noise variance
0.02 0.03 0.04 0.05 0.06 0.07 Speckled image 0.6397 0.5495 0.4875 0.4633 0.4241 0.3714 Median(3x3) 0.6259 0.5728 0.5346 0.4470 0.4424 0.4154 Median(5x5) 0.5660 0.5268 0.4647 0.4268 0.3981 0.3538 HMF(3x3) 0.7552 0.6746 0.6189 0.5441 0.5197 0.4911 HMF(5x5) 0.7723 0.6806 0.6106 0.5490 0.5065 0.4856 Lee 0.3318 0.3061 0.2795 0.2719 0.2678 0.2476 Kuan 0.3342 0.3050 0.2856 0.2771 0.2664 0.2363 Frost 0.5241 0.4627 0.4069 0.3824 0.3480 0.3338 NCD 0.7662 0.6444 0.5594 0.5100 0.4667 0.4335 MHMF 0.7631 0.6670 0.6177 0.5799 0.5411 0.5146 AWHMF 0.8036 0.7268 0.6785 0.6253 0.5787 0.5304
45
Table 2.4 CoC values obtained for Test Image 1
Correlation Coefficient(CoC)
Filters Noise variance
0.02 0.03 0.04 0.05 0.06 0.07 Speckled image 0.9662 0.9502 0.9350 0.9223 0.9066 0.8897 Median(3x3) 0.9718 0.9672 0.9617 0.9573 0.9506 0.9468 Median(5x5) 0.9552 0.9517 0.9449 0.9449 0.9382 0.9361 HMF(3x3) 0.9802 0.9706 0.9624 0.9513 0.9450 0.9359 HMF(5x5) 0.9791 0.9714 0.9634 0.9575 0.9508 0.9445 Lee 0.9715 0.9691 0.9662 0.9637 0.9626 0.9589 Kuan 0.9719 0.9688 0.9660 0.9639 0.9623 0.9590 Frost 0.9762 0.9707 0.9652 0.9622 0.9567 0.9526 NCD 0.9826 0.9698 0.9540 0.9405 0.9282 0.9124 MHMF 0.9814 0.9729 0.9664 0.9595 0.9504 0.9427 AWHMF 0.9848 0.9783 0.9729 0.9659 0.9601 0.9534
Table2.5 FSIM values obtained for Test Image 1
Feature Similarity (FSIM) Index
Filters Noise variance
0.02 0.03 0.04 0.05 0.06 0.07 Speckled image 0.9870 0.9823 0.9785 0.9755 0.9722 0.9699 Median(3x3) 0.9887 0.9851 0.9831 0.9803 0.9802 0.9768 Median(5x5) 0.9890 0.9846 0.9817 0.9828 0.9802 0.9788 HMF(3x3) 0.9889 0.9847 0.9823 0.9782 0.9769 0.9735 HMF(5x5) 0.9913 0.9890 0.9873 0.9838 0.9817 0.9803 Lee 0.9920 0.9890 0.9876 0.9857 0.9833 0.9807 Kuan 0.9919 0.9891 0.9880 0.9865 0.9842 0.9813 Frost 0.9923 0.9895 0.9881 0.9867 0.9851 0.9821 NCD 0.9927 0.9897 0.9852 0.9806 0.9769 0.9737 MHMF 0.9905 0.9884 0.9850 0.9831 0.9817 0.9788 AWHMF 0.9939 0.9906 0.9885 0.9843 0.9821 0.9790
46
Edge Preservation Index (EPI) is used to test the edge preservation
ability of the filters. The highest value of EPI indicates that the filter is good
in preserving edges. The EPI values of various speckle reduction filters for
different noise variances are listed in Table2.3. From the Table, it is clear that
the MHMF preserves edges better than the standard speckle filters (Lee, Kuan
and Frost) and NCD. The proposed AWHMF outperforms the other
algorithms in terms of EPI.
The Correlation Coefficient (CoC) is a quantitative measure, which
provides the correlation between the original image and the denoised image.
The CoC of various filters is given in Table 2.4. The value of CoC is higher,
if both the images are perfectly identical. From the table it can be observed
that the AWHMF performed better than the existing filters up to noise
variance of 0.05. At higher noise variance the performance of Lee and Kuan
was found to be good. The FSIM values in Table 2.5 show that the AWHMF
is able to preserve the features only at lower noise levels and at higher noise
levels the Frost filter performs well.
For subjective evaluation, the output images of different spatial
domain filters for noise variance of 0.02 are shown in Figure 2.5. From the
figures it is evident that the proposed filters are able to preserve edges and
fine details.
47
`
Figure 2.5 Original, noisy and denoised images for Test Image 1
Test Image 3 and Test Image 4: The performance of the proposed algorithm
MHMF and AWHMF is tested using Brain images (Coronal View - Test
Image 3 and Sagittal View - Test Image 4).
The plot of PSNR values of the proposed and the existing denoising
algorithms against different noise variances for Test image 3 is given in
Figure 2.6. From this plot, it is inferred that the proposed AWHMF algorithm
performs better than the other denoising algorithms. Table 2.6lists the RMSE
values of different algorithms and the lower values of RMSE obtained by
AWHMF indicates that the error is less in the despeckled image.
(c) Median (3x3) (d)Median (5x5)
(e) HMF (3x3) (f) HMF (5x5) (g) Lee filter (h)Kuan filter
(a)Test Image 1 (b)Noisy-0.02
(i) Frost filter (k) MHMF (l) AWHMF (j)NCD
48
Figure 2.6 Plot of PSNR values for Test Image 3
Table 2.6 RMSE values obtained for Test Image 3
Root Mean Square Error (RMSE)
Filters Noise variance
0.02 0.03 0.04 0.05 0.06 0.07 Speckled image 0.0392 0.0478 0.0555 0.0620 0.0681 0.0730 Median(3x3) 0.0332 0.0366 0.0386 0.0420 0.0443 0.0476 Median(5x5) 0.0424 0.0437 0.0449 0.0468 0.0479 0.0484 HMF(3x3) 0.0307 0.0358 0.0409 0.0451 0.0484 0.0517 HMF(5x5) 0.0305 0.0347 0.0378 0.0408 0.0431 0.0469 Lee 0.0407 0.0423 0.0430 0.0447 0.0446 0.0458 Kuan 0.0413 0.0419 0.0430 0.0443 0.0454 0.0461 Frost 0.0298 0.0325 0.0358 0.0388 0.0435 0.0434 NCD 0.0315 0.0370 0.0432 0.0498 0.0557 0.0613 MHMF 0.0337 0.0408 0.0464 0.0516 0.0563 0.0600 AWHMF 0.0264 0.0305 0.0338 0.0370 0.0401 0.0429
0.02 0.03 0.04 0.05 0.06 0.075
10
15
20
25
30
35
40
Noise Variance
HMF(3x3)LeeFrostNCDMHMFAWHMF
49
Table 2.7 EPI values obtained for Test Image 3
Edge Preservation Index (EPI)
Filters Noise variance
0.02 0.03 0.04 0.05 0.06 0.07 Speckled image 0.5964 0.5179 0.4563 0.4218 0.3877 0.3373 Median(3x3) 0.2918 0.2459 0.2188 0.1716 0.1398 0.1047 Median(5x5) 0.0815 0.0851 0.0622 0.0281 0.0334 0.0036 HMF(3x3) 0.5597 0.4861 0.4193 0.3758 0.3438 0.3114 HMF(5x5) 0.5541 0.4608 0.4128 0.3558 0.3524 0.2877 Lee 0.1356 0.1241 0.1194 0.1076 0.1191 0.1098 Kuan 0.1421 0.1413 0.1382 0.1231 0.1081 0.1178 Frost 0.3695 0.3326 0.2920 0.2543 0.2306 0.2246 NCD 0.6017 0.5366 0.4972 0.4359 0.4020 0.3886 MHMF 0.6314 0.5719 0.5237 0.4741 0.4269 0.4218 AWHMF 0.6563 0.5831 0.5284 0.4800 0.4374 0.4392
Figure 2.7 Plot of CoC values for Test Image 3
0.02 0.03 0.04 0.05 0.06 0.070.8
0.82
0.84
0.86
0.88
0.9
0.92
0.94
0.96
0.98
Noise Variance
HMF(3x3)LeeFrostNCDMHMFAWHMF
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Table 2.8 FSIM values obtained for Test Image 3
Feature Similarity Index (FSIM) Filters Noise variance
0.02 0.03 0.04 0.05 0.06 0.07 Speckled image 0.9900 0.9853 0.9793 0.9758 0.9716 0.9669 Median(3x3) 0.9905 0.9875 0.9862 0.9821 0.9792 0.9749 Median(5x5) 0.9781 0.9778 0.9766 0.9751 0.9742 0.9730 HMF(3x3) 0.9912 0.9873 0.9838 0.9784 0.9754 0.9705 HMF(5x5) 0.9917 0.9889 0.9877 0.9840 0.9820 0.9799 Lee 0.9896 0.9883 0.9870 0.9842 0.9847 0.9823 Kuan 0.9893 0.9886 0.9868 0.9863 0.9840 0.9830 Frost 0.9936 0.9915 0.9898 0.9867 0.9851 0.9843 NCD 0.9925 0.9909 0.9876 0.9842 0.9804 0.9749 MHMF 0.9937 0.9907 0.9866 0.9848 0.9813 0.9784 AWHMF 0.9940 0.9927 0.9899 0.9859 0.9835 0.9821
The EPI values for Test Image 3 at different noise levels are
presented in Table 2.7. The highlighted values indicate that the proposed filter
AWHMF is good in preserving edges. From the plot of CoC in Figure 2.7, it
can be observed that the performance of AWHMF is better than the other
filters. In Table 2.8, the higher values of FSIM indicate that the AWHMF is
able to preserve features effectively at lower noise levels.
For subjective evaluation, the output images of different spatial
domain filters are shown in Figure 2.8. From the figure, it is observed that the
AWHMF improves the quality of the image.
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Figure 2.8 Original, noisy and despeckled images for Test Image 3
Table 2.9 shows the PSNR values obtained for the Test image 4 and is observed that the AWHMF gives better PSNR values under different noise conditions. For higher noise variance (0.07), the MHMF yields better performance in terms of PSNR values.
The RMSE values of different filters obtained for Test Image 4 are shown in Table2.10. From the table, it is observed that the filters AWHMF and MHMF give better performance as compared to others.
The EPI values of different filters are listed in Table 2.11. For low and moderate noise levels the proposed filter AWHMF exhibits high performance and when the noise level is high, the standard filters Lee and Kuan perform well.
(c) Median (3x3) (d) Median (5x5)
(e) HMF (3x3) (g) Lee filter (h) Kuan filter (f) HMF (5x5)
(l)AWHMF (i) Frostfilter
(b)Noisy -0.02 (a)Test image 3
(k) MHMF (j)NCD
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Table 2.9 PSNR values obtained for Test Image 4
Peak Signal to Noise Ratio (PSNR) in dB Filters Noise variance
0.02 0.03 0.04 0.05 0.06 0.07 Speckled image 27.59 25.88 24.65 23.79 22.98 22.28 Median(3x3) 30.26 29.09 28.47 27.12 26.97 26.76 Median(5x5) 28.51 28.08 27.48 27.25 26.84 26.41 HMF(3x3) 30.46 28.79 27.67 26.80 26.00 25.43 HMF(5x5) 30.73 29.59 28.58 27.85 27.09 26.64 Lee 27.21 27.06 26.74 26.48 26.36 26.08 Kuan 27.25 27.13 26.78 26.65 26.25 26.17 Frost 30.80 30.13 28.95 28.17 27.31 26.67 NCD 29.29 27.22 25.74 24.68 23.81 23.04 MHMF 31.42 29.97 29.18 28.52 27.89 27.39 AWHMF 31.89 30.42 29.39 28.59 27.91 27.36
Table 2.10 RMSE values obtained for Test Image 4
Root Mean Square Error (RMSE) Filters Noise variance
0.02 0.03 0.04 0.05 0.06 0.07 Speckled image 0.0590 0.0718 0.0828 0.0914 0.1003 0.1087 Median(3x3) 0.0387 0.0442 0.0503 0.0556 0.0591 0.0642 Median(5x5) 0.0531 0.0557 0.0598 0.0614 0.0643 0.0676 HMF(3x3) 0.0424 0.0514 0.0585 0.0646 0.0709 0.0757 HMF(5x5) 0.0411 0.0469 0.0526 0.0573 0.0625 0.0659 Lee 0.0617 0.0627 0.0651 0.0670 0.0680 0.0703 Kuan 0.0614 0.0623 0.0648 0.0657 0.0688 0.0695 Frost 0.0372 0.0440 0.0505 0.0552 0.0609 0.0656 NCD 0.0485 0.0616 0.0730 0.0824 0.0912 0.0996 MHMF 0.0380 0.0449 0.0491 0.0530 0.0570 0.0604 AWHMF 0.0360 0.0426 0.0480 0.0526 0.0569 0.0606
53
Table 2.11 EPI values obtained for Test Image 4
Edge Preservation Index (EPI) Filters Noise variance
0.02 0.03 0.04 0.05 0.06 0.07 Speckled image 0.3648 0.2991 0.2734 0.2402 0.2263 0.2098 Median(3x3) 0.4940 0.4260 0.3760 0.3290 0.3349 0.2941 Median(5x5) 0.3636 0.2921 0.2536 0.2376 0.2165 0.1865 HMF(3x3) 0.4493 0.3749 0.3440 0.2982 0.2769 0.2570 HMF(5x5) 0.4163 0.3455 0.2933 0.2606 0.2473 0.2305 Lee 0.4557 0.4307 0.4265 0.3992 0.3860 0.3634 Kuan 0.4509 0.4391 0.4077 0.3883 0.3879 0.3551 Frost 0.4735 0.3933 0.3575 0.3145 0.2949 0.2681 NCD 0.4261 0.3517 0.2984 0.2618 0.2540 0.2226 MHMF 0.4528 0.3738 0.3332 0.3115 0.2746 0.2655 AWHMF 0.5288 0.4562 0.4300 0.3999 0.3383 0.3028
Table 2.12 CoC values obtained for Test image 4
Correlation Coefficient (CoC) Filters Noise variance
0.02 0.03 0.04 0.05 0.06 0.07
Speckled image 0.9352 0.9071 0.8805 0.8599 0.8366 0.8089
Median(3x3) 0.9703 0.9609 0.9494 0.9384 0.9305 0.9178
Median(5x5) 0.9484 0.9423 0.9321 0.9267 0.9188 0.9096
HMF(3x3) 0.9642 0.9480 0.9337 0.9204 0.9057 0.8907
HMF(5x5) 0.9666 0.9558 0.9438 0.9339 0.9213 0.9130
Lee 0.9221 0.9194 0.9127 0.9074 0.9047 0.8983
Kuan 0.9227 0.9204 0.9140 0.9110 0.9023 0.9004
Frost 0.9741 0.9633 0.9535 0.9441 0.9347 0.9258
NCD 0.9541 0.9285 0.9033 0.8805 0.8588 0.8338 MHMF 0.9724 0.9612 0.9511 0.9428 0.9340 0.9255
AWHMF 0.9940 0.9921 0.9888 0.9840 0.9831 0.9792
54
Figure 2.9 Plot of FSIM for Test Image 4
Table 2.12 lists the CoC values of different speckle reduction
filters. The CoC values of AWHMF indicate that its performance is better
than the other filters.
The performance of the proposed filters and some high performing
filters in terms FSIM is illustrated in Figure 2.9. From the figure it is obvious
that the proposed filter AWHMF gives better performance than the other
filters.
The despeckled images of different spatial domain filters are given
in Figure 2.10, and it is clear from the figure that the image quality is
improved by the AWHMF when compared to other filters.
0.02 0.03 0.04 0.05 0.06 0.070.975
0.98
0.985
0.99
0.995
1
Noise Variance
Median(3x3)HMF(3x3)LeeFrostMHMFAWHMF
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Figure 2.10 Original, noisy and despeckled images for Test Image 4
Ultrasound Images: The proposed methods are tested with ultrasound
imagesof Liver, Breast and Gall bladder. The original and despeckled images
obtained using some high performing filters are illustrated in figures from
Figure 2.11 to Figure 2.13. Speckle Suppression Index (SSI) is used to
measure the quality of the resultant images.
(a)Test image 4
(h) AWHMF
(b)Noisy -0.02 (c)Median (3x3)
(e)HMF (3x3) (g) MHMF (f) NCD
(d) Lee Filter
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.
Figure 2.11 Original and despeckled images of ultrasound image of Liver
(b)Frost (c) NCD
(d) MHMF (e) AWHMF
(a) Original image - Liver
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Figure 2.12 Original and despeckled images of ultrasound image of Breast
(c) NCD (b) Frost
(d) MHMF (e) AWHMF
(a)Original image - Breast
58
Figure 2.13 Original and despeckled images of ultrasound image of Gall bladder
(d) MHMF
(a) Original Image
(b) Frost (c) NCD
(e) AWHMF
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Figure 2.14 shows the plot of SSI values obtained for ultrasound
images of Liver, Breast and Gall bladder. From the figure, it is observed that
the SSI values of AWHMF are less when compared to the other filters such as
Frost, NCD and MHMF and indicates that the AWHMF suppresses speckle
noise effectively.
Figure 2.14 Plot of SSI for ultrasound images
Execution Time: The execution time taken by a filter is an important
measure to find its computational complexity, and depends on the computing
-period. In addition to the clock-period, it also depends on
the memory-size, the input data size, and the memory access time, etc. The
proposed algorithm has been implemented in MATLAB 7.12.0 environment
with Intel core i3@ 2.40 GHz processor with 2GB RAM. The execution time
of the proposed and the existing spatial domain speckle reduction algorithms
for different test images with speckle noise of variance 0.04 is illustrated in
Table 2.13. From the table, it is evident that the execution time of MHMF is
less than the standard filters for speckle reduction and higher than the
traditional median filter.
0.95
0.96
0.97
0.98
0.99
1
Fros
t
NCD
MH
MF
AW
HM
F
Fros
t
NCD
MH
MF
AW
HM
F
Fros
t
NCD
MH
MF
AW
HM
F
Liver Breast Gall Bladder
SSI
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Table 2.13 Execution Time
Execution Time in Seconds
Method Test image1
( 128 x 128)
Test image3
(128x128)
Test image4
(128x128)
Median(3x3) 0.366 0.379 0.378
Median(5x5) 0.382 0.399 0.379
HMF(3x3) 0.886 0.882 0.881
HMF(5x5) 0.917 0.916 0.926
Lee(3x3) 1.531 1.544 1.526
Kuan(3x3) 1.524 1.524 1.545
Frost(3x3) 0.875 0.896 0.882
NCD 0.635 0.624 0.623
MHMF (5x5) 0.689 0.691 0.684
AWHMF 0.991 0.994 0.993
2.5 CONCLUSION
In this chapter two spatial domain filters MHMF and AWHMF are
proposed for speckle reduction in ultrasound images. The experimental results
reveal that the AWHMF gives better performance for different levels of
speckle noise. PSNR values are higher (1dB) for low noise levels and under
such noise conditions the filters have smaller RMSE values. AWHMF also
gives superior performance in terms of EPI and which can be observed from
the tables. From the FSIM and CoC values obtained, it is clear that the
proposed filter AWHMF is good in feature preservation when compared to
the other spatial filters. It is also observed from the tables that the other
proposed filter MHMF shows only moderate performance in terms of PSNR,
RMSE and EPI. But its execution time is minimal as compared to the standard
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filters. The performance of AWHMF is good at lower levels of speckle noise
(0.02 to 0.05). The time taken to execute AWHMF is slightly higher than the
HMF and Frost filters and less than the standard filters namely Lee and Kuan.
The proposed filters efficiency is tested for the ultrasound images
collected from hospitals and taken from repository. The effectiveness of the
filters is proved with the computation of SSI, which is less in case of
AWHMF. Based on the above data and the related discussions, it may be
concluded that AWHMF works well when the speckle noise variance is low
and also preserves the edges and minute details effectively. When the noise
variance increases, it merges with the high frequency information of the
image content and hence it is difficult for AWHMF to perform better at
higher noise levels.