The document discusses a modified anisotropic diffusion filter developed for reducing speckle noise in ultrasound images, with a focus on its theoretical background and application results. It highlights the effectiveness of the proposed filter in enhancing signal-to-noise ratio (SNR) and image quality indexes across various types of ultrasound images, while also noting limitations related to its application on different imaging modalities. The conclusion emphasizes the potential for future improvements and broader applications in noise reduction.

1. 1
Speckle Noise Reduction in Ultrasound Images using Adaptive and
Anisotropic Diffusion filter
Submitted By
Md. Shohel Rana
CE-06006
2005-06
Supervised By
Dr. Md. Motiur Rahman
Associate Professor
Dept. of CSE
MBSTU

2. 2
Motivation and Contribution
 US Imaging Technique less cost
 Nonlinear and Anisotropic filter for removing speckle noise can be
removed from US images
 Proposed a modified Anisotropic filter which reduce speckle noises

3. 3
Speckle Noise
 Medical images are usually corrupted by noise during their
acquisition and transmission.
 Affects all coherent imaging systems, including medical
ultrasound.
 Acquired image is corrupted by a random granular pattern.
 A possible generalized model of the speckle imaging is
Where g , f , u and ξ stand for the observed image, original image,
multiplicative component and additive component of the speckle noise,
respectively.
( , ) ( , ) ( , ) ( , )g n m f n m u n m n mξ= +

4. 4
US Image Measurement Metrics
 SNR : Signal to Noise Ratio compares the level of desired signal to the level of
background noise
 RMSE : The Root Mean square error is given by
 PSNR : Peak Signal to Noise Ratio is computed by
22
, ,
1 1
10 2
1 1
, ,
( )
10log
( )
M N
i j i j
i j
M N
i j
i j i j
SNR
yx
yx
= =
= =
+
= =
∑∑
−∑∑
2
1 1
, ,
1
( )
M N
i j
i j i jRMSE
MN
yx
= =
= −∑∑
2
10
20 ( )logPSNR RMSEg=

5. US Image Measurement
Metrics(Cont.)
 IMGQ : The image quality index is given by
 SSIM : The Structural Similarity Index between two images is
computed as
 PT : To compare edge preservation performances of different
speckle reduction schemes, the parameter of transition
2 2 22
22
( ) ( )
xy y x
x y yx
y x
IMGQI
y x
σ σ σ
σ σ σσ
=
+ +
2 1
2 1
PT
µ µ
µ µ
−
=
+
1 2
2 2 2 2
1 2
(2 )(2 )
( )( )
xyx y
x yx y
SSIM
C C
C C
µ µ σ
µ µ σ σ
+ +
=
+ + + +

6. 6
Filtering On US Image
 The Lee and Kuan filters produce the enhancement data
according to
Where W is the weighting function ranging between 0 for flat regions and
1 for regions with high signal activity, is the average of pixels in a
moving window and is the output of the filter.
ˆ( ) ( ) [ ( ) ( )] ( )R t I t I t I t W t= + − ×
I
ˆ( )R t

7. 7
Filtering On US Image(Cont.)
 Lee filter
The weighting function for the Lee filter is
 Kuan Filter
The weighting function of the kuan filter is defined as
Where and are the coefficients of variations of noise u and
image I
 Frost Filter
The image Z[i, j] is modeled by frost as
Where h i j, is system impulse response and * denotes convolution
2
2
( ) 1
( )
u
I
W t
t
C
C
= −
2
2
2
1
( )
( )
1
u
I
u
t
W t
C
C
C
−
=
+
I
I
I
C
σ=u
u
u
C
σ=
, , , ,[ . ]*i j i j i j i jn hZ Z=

8. Filtering On US Image (Cont.)
 Frost Filter (Cont.)
Minimum mean square filter has the form
Where m(t ) function is an isotropic impulse response
Where K1 is a normalizing constant and α is the decay constant correlation
coefficient between adjacent pixels of the original is image x(t) and t
corresponds to the distance between pixels in the spatial domain.
ˆ( ) ( )* ( )x t z t m t=
1( ) exp( )m t tK α α= −

9. 9
Anisotropic Diffusion Filter (Cont.)
 In Image Procesing and Computer Vision, Anisotropic
Diffusion, also called Perona–Malik diffusion.
 A technique aiming at reducing image noise without removing
significant parts of the image content, typically edges.
 Anisotropic diffusion is an efficient nonlinear technique for
simultaneously performing contrast enhancement and noise
reduction. It smoothes homogeneous image regions and retains
image edges.
( )[ ]
( )



==
∇⋅∇=
∂
∂
00 ItI
IIcdiv
t
I

10. 10
Anisotropic Diffusion Filter (Cont.)
 Pietro Perona and Jitendra Malik pioneered the idea of
anisotropic diffusion in 1990 and proposed two functions for
the diffusion coefficient
and
 The anisotropic diffusion method can be iteratively
applied to the output image:
( ) ( )
( )
( ) ( ) ( )
( ) ( )
( )
( ) ( ) ( )
( ) ( ) 







∇⋅∇+∇⋅∇+
∇⋅∇+∇⋅∇
×+=+
n
South
n
South
n
West
n
West
n
East
n
East
n
North
n
Northnn
IIcIIc
IIcIIc
II λ1
( )
( )2
/1
1
kI
Ic
∇+
=∇( ) ( )[ ]2
/||exp|| kIIc ∇−=∇

11. 11
Anisotropic Diffusion Filter (Cont.)
SRAD
 Allows the generation of an image scale space without bias due to filter
window size and shape.
 Preserves edges and enhances edges by inhibiting diffusion across edges and
allowing diffusion on either side of the edge.
 Related directly to the Lee and Frost window-based filters.
 The edge sensitive extension of conventional adaptive speckle filter
 The automatic determination of q0(t) is desired in real applications to
eliminate heuristic parameter choice
Where is a constant, and q0(t) is the speckle coefficient of variation in the observed
image.
*
0 0
( ) t
tq q e
ρ−
≈
ρ

12. Anisotropic Diffusion Filter (Cont.)
 SRAD (Cont.)
The discrete isotropic diffusion update is
Assuming that pixels in the region are statistically independent and identically
distributed and the local means remains the same before and after an iteration
So the final updating equation is
Where is the divergence.
ρ
, , 1, 1, , 1 , 1 ,( 4 )
4
t t t t t t t t
i j i j i j i j i j i j i j
t
I I I I I I I
+∆
+ − + −
∆
= + + + + −
2
2
( ) ( )
4
( )(1 )o o
t t t
tq q t+∆ = +
∆−∆
1
, , ,
4
nn n
i j i j i j
t
dI I
+ ∆
= +
,
n
i jd

13. 13
Experiment and Result (Cont.)
Input and Output
Input and Output of
Abdomen image for
speckle noise (0.04) in
various filtering

14. Experiment and Result (Cont.)
Input and Output
Input and Output of
Ortho image for
speckle noise (0.04) in
various filtering

15. Experiment and Result (Cont.)
Input and Output
Input and Output of
Liver_GB image for
speckle noise (0.04) in
various filtering

16. Experiment and Result (Cont.)
Input and Output
Input and Output of
Kidney image for
speckle noise (0.04) in
various filtering

17. Experiment and Result (Cont.)
Input and Output
Input and Output of
Brest image for
speckle noise (0.04) in
various filtering

18. Experiment and Result (Cont.)
Input and Output
Input and Output of
Prostrate image for
speckle noise (0.04) in
various filtering

19. 19
Experiment and Result (Cont.)
.

20. 20
Proposed Filter
In the case of proposed filtering is the modified version of
anisotropic diffusion filtering the direction and strength of the
diffusion are controlled by an edge detection function
Algorithm
1. Input image with or without speckle noise
2. Choose a kernel or window of size 5*5 or 3*3.
3. Set the kernel or window to the noisy image and replace each
pixel value of image by the following equation
0[1: ] [1: ]
( )
( )
n
sort n
mid sort
F MN
sort
mid
W I
W W
I I
=
=
=

21. 21
Proposed Filter (Cont.)
Algorithm (Cont.)
4. Calculate gradient in all directions (N,S,E,W) of Processed image Imid .
5. Calculate Diffusion coefficients in all directions according to the method
using proposed modified equation.
6. Finally follow the following equation
2
1
(|| ||)
1
|| ||
mid
mid
C I
I
K
∆ =
+
∆
( ) ( )
( ) ( )
0
North mid North mid East mid East mid
out mid
West mid West mid South mid South mid
c c
c c
I I I I
I I I
I I I I
λ
 ∇ ×∇ + ∇ ×∇
 = + + ×
 + ∇ ×∇ + ∇ ×∇ 

22. 22
Proposed Filter (Cont.)
Input and Output
Input and Output of
all image for speckle
noise (0.04) in
proposed filter

23. 23
Proposed Filter (Cont.)

24. Limitation
 My proposed modified filter gives best result of SNR, SSIM and IMGQ for
all types of ultrasound images but not of RMSE, PSNR, PT for all images.
 It has been demonstrated that proposed modified filter is capable of
reducing speckle noise but not for other types of image.
 It has been demonstrated that proposed modified filter is used for only
Ultrasound images but not for CT, MRI, X-RAY and so on.
 It has been demonstrated that proposed modified filter is capable of
reducing speckle noise on 2D images but not 3D, 4D.
 Used images’ extension was “.tif”.

25. 25
Conclusion And Future Work
 It has been demonstrated that proposed filter is capable of reducing
speckle noise.
 My proposed modified filter gives Signal to Noise Ratio (SNR) value is
best for all six (Abdomen, Ortho, Liver_GB, Kidney, Brest and Prostrate)
types of US images as well as gives the best result for Image Quality
Index (IMGQI) and Structural Similarity Index (SSIM).
 It can be used in 3D,4D Ultrasound images.
 Trying to remove all types of noises from images.

26. THANKS
Do You have any question please!!!