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Despeckling Of Ultrasound
Images
Ronen Tur
Outline
Ultrasound Imaging What Is Speckle Noise? Standard Denoising Methods Modified Homomorphic
Despeckling
Papers Michailovich O. & Tannenbaum A.,
“Despeckling of Medical Ultrasound Images”, IEEE transactions on ultrasonics, ferroelectrics and frequency control, vol. 53, no.1, january 2006
Quistgaard J., “Signal Acquisition and Processing in Medical Diagnostic Ultrasound”, IEEE Sig. Proc., jan. 1997
ULS Imaging - Motivation
Non-invasive Non-ionizing radiation (CT) Cheap (vs. expensive MRI) Real-time imaging
Tracking Monitoring during treatment
Portable platforms
ULS Physics
Acoustic impedance Different tissue Different
impedance Reflection
Desired picture: reflectivity function Denote it by
Z c
2 1
2 1
Z ZR
Z Z
( )r
"...וכל העם רואים את הקולות"(פרשת השבוע)
ULS Physics
cannot be measured directly Pulse-echo imaging 4 steps:
Transmission Reflection Reception Estimation
( )r
( )r
1D
x( )p t
1D
– transmitted pulse – reflectivity coefficient at x – received signal( )x( )p t
( )y t
20
( ) ( ) ( 2 ) ( ) ( )x ct
y t x p t x c dx x p x
x0x
( )p t
1D
– transmitted pulse – reflectivity coefficient at x – received signal
Estimation: For the case ,
( )x( )p t
( )y t
20
( ) ( ) ( 2 ) ( ) ( )x ct
y t x p t x c dx x p x
0 0ˆ ( ) (2 )x y x c ( ) ( )p t t 0 0
ˆ ( ) ( )x x
x0x
( )p t
2D
Complex problem Sum over different ( )r
max /2
0 /2
( ) ( 2 ) ( , )R
y t p t r c r d dr
( )r
maxR
2
2D - Beamforming Array of N
elements - ith signal
received Problem:
Given Estimate
1( )
N
i iy t
( )r
( )iy t( )r
2D - Beamforming Approximation of
inverse scattering solution
- round trip to the ith element
Result called RF-image
( )r
1
ˆ ( ) ( )N
i ii
r y t
it
t
Envelope Detection Carrier freq.
~5MHz Information in the
envelope Demodulation Take the absolute
value
PSF – Point Spread Function
Defined for any imaging system PSF - the impulse response of the
system Ideal: Delta function Realistic: Has a blurring effect
Example
Noise In Ultrasound
Major disadvantage of ULS imaging Where does the noise come from?
Speckle Noise
Coherent imaging 1960 – Operation of the first laser Objects viewed by coherent light
have granular appearance Unrelated to macroscopic structure What drives this phenomena?
"...היהפוך כושי עורו, נמר חברבורותיו"(ירמיה י"ג/כ"ג)
Speckle Noise – Cont.
1977 – Goodman’s paper on speckle
Roughness on the order of a wavelength
Many independent scatterers Interference occurs
Visualization
Speckle Noise – Cont.
1977 – Goodman’s paper on speckle
Roughness on the order of a wavelength
Many independent scatterers Interference occurs Signal dependent noise
Denoising Speckles
Old methods Linear filtering Median filtering Image is smoothed as well
The giant leap… Speckle noise is multiplicative! Denoise the log of the image instead
Homomorphic Denoising
Original After Denoising
Noise Statistics
Standard denoising assume WGN This is not the case Proposed method:1. Preprocess input
a. “Flatten” the noise (White)b. Gaussianize the noise (Gaussian)
2. Use usual denoising schemes (WGN) Reflectivity func. remains unchanged
Mathematical Model Assuming LSI Convolution with PSF Model: - the axial and lateral indices, resp. - the RF-image - the tissue reflectivity function - Point Spread Function (PSF) - additive noise
( , ) ( , ) ( , ) ( , )g n m f n m h n m u n m
,n m
g
f
h
u
LSI Assumption
Linearity usually holds, but… The system is NOT shift invariant!!!
e.g. Radial – freq. dependent attenuation Solution: segmentation
Deal with one segment at a time Each small segment is LSI
w.l.o.g. we shall deal with one segment
Power Spectral Densities
Model:2
1 2 1 2 1 2 1 2( , ) ( , ) | ( , ) | ( , )g f uP w w P w w H w w P w w
( , ) ( , ) ( , ) ( , )g n m f n m h n m u n m
Power Spectral Densities
Assuming lack of correlation between: Image samples (variance ) Noise samples (variance )
21 2 1 2 1 2 1 2( , ) ( , ) | ( , ) | ( , )g f uP w w P w w H w w P w w
2 2 21 2 1 2( , ) | ( , ) |g f uP w w H w w
2f
2u
Power Spectral Densities
Assuming lack of correlation between: Image samples (variance ) Noise samples (variance )
PSD of reconstructed image isn’t white! Defined by the PSF Has non-negligible support
21 2 1 2 1 2 1 2( , ) ( , ) | ( , ) | ( , )g f uP w w P w w H w w P w w
2 2 21 2 1 2( , ) | ( , ) |g f uP w w H w w
2f
2u
Correlation Visualization
Preproc. 1st Step - Decorrelation
Speckle noise is not white Either take correlation into
account, or.. Perform decorrelation Apply the linear filter:
“Flattens” the PSD of the image
1 2 1 22 2 21 2
1( , )
| ( , ) | u f
L w wH w w
Preproc. 1st Step - Decorrelation
Speckle noise is not white Either take correlation into account,
or.. Perform decorrelation Apply the linear filter:
“Flattens” the PSD of the image Chosen empirically
1 2 1 22 2 21 2
1( , )
| ( , ) | u f
L w wH w w
Decorrelation ExamplePhantom Image Input Image
Input Image Output of stage I
Decorrelation Example
PSF Estimation
PSF required for filter Blind deconvolution methods
Based on smoothness properties of PSF w.r.t. the reflectivity function
Generalized Model
Model for speckled images
Additive term may be neglected Thus we have:
( , ) ( , ) ( , ) ( , )g n m f n m u n m n m
( , ) ( , ) ( , )g n m f n m u n m
Good Old Additive Noise
Taking the log:
Subscript denotes the log Problem: rejection of additive noise
But what are the noise statistics?
( , ) ( , ) ( , )l l lg n m f n m u n m
Log Transformed Speckles
Noise statistics – no consensus Many scatterers per resolution cell
Rayleigh distribution Many scatterers per resolution cell
Various non-Rayleigh distributions Rician, K, Nakagami…
Generalized Gamma dist.
Contains several relevant distributions
Fasten your seat-belts…
Generalized Gamma dist.
Contains several relevant distributions
Fasten your seat-belts… ( ) exp ( ln ) exp ( ln )( )Yp y y y
Examples Of Distributions
Preproc. 2nd Step - Shrinkage
Noise resembles Gaussian, with few outliers
Proposition: Perform outlier-shrinkage Afterwards, deal with noise as WGN
Outlier-Shrinkage
Apply median filter, diff. denoted Calculate residuals:
Final result of shrinkage: That’s it
Standard WGN denoising should work now
G
, , ,, ,
0 ,
G n m G n mR n m sign G n m
else
( )G R
Block Diagram
In Silico Results
In Silico Results
In Vivo Results
In Vivo Results
Thank you…
Any questions?
Discussion Is speckle noise multiplicative?
Only under specific conditions Model it better…
Real-time applicability Differentiate between
Real reflectors And speckle scattering Using sparsity constraints
Optional: Quantitative Assesment
In silico: NMSE – Normalized MSE Speckle SNR – ration of mean to std. Beta – measure of preservation of
sharp details In vivo:
Speckle SNR – ration of mean to std. Alpha – evaluate resolution
Exploring Speckles
רעש חברבורות Coherent imaging Rough object
Roughness on the order of a wavelength Many scatterers within resolution cell Pattern determined by imaging
system! Signal dependent noise
"...היהפוך כושי עורו, נמר חברבורותיו"(ירמיה י"ג/כ"ג)
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