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)