104/19/23

Three-dimensional Quantitative Ultrasound Imaging

A.J. Devaney

Department of electrical and computer engineering

Northeastern university

Boston, MA 02115

Devaney@ece.neu.edu

“Acoustical Holography,” Encyclopedia of Applied Physics,Americal Institute of Physics 1993.

“Acoustical Holography,” Encyclopedia of Applied Physics,Americal Institute of Physics 1993.

A.J. Devaney Associates, Inc. 295 Huntington Ave-suite 208. Boston, MA 02115

Tonydev2@aol.com

204/19/23

Canonical Imaging Configuration

Insonifying waveform

Scattered wavefield

Sensor system

( ) ( , ) ( , ) ( , )

( , ) [ ( , )]

2 2

2 21

k O

O k n

r r r

r r

Quantitative imaging problem: Given set of scattered field measurements determine object function

304/19/23

Data Model

( , ) ( , ) ( , )

( , ) ' ( ' , ) ( ' , )| ' |

| ' |

r r r

r r rr r

r r

ins

s d r Oeik1

43

• Nonlinear and nonlocal mapping from object function to scattered field• Mapping from 3D to 2D thus non-unique

Born approximation Rytov approximation

Born approximation Rytov approximation

bs

ind r Oeik

( , ) ' ( ' , ) ( ' , )| ' |

| ' |r r r

r r

r r

14

3

404/19/23

Born Approximation Imaging

|'|

|'|),'(),'('),( 3

41

rr

rrrrr

ikeOrd in

sb

),'(),'(),'('),(),( 3 rrrrrr hOrd inIsb

scattering point Image point

1

4eik

h| ' |

| ' |( ' , )

r r

r rr r

“Lens”outgoing spherical wave Incoming spherical wave

.

504/19/23

Analog Two-dimensional Imaging

Object Image

x,y x,y

Lens

( , ) ' ' ( ' , ' ) ( ' , ' )I x y dx dy h x x y y I x y

Lens converts outgoing spherical waves into incoming spherical wavesto produce the image field.

604/19/23

Backpropagation Imaging

Sensor system aperture

Scattered wavefieldObject

rsssr ikeAds ),(),(

1. Measure wavefield over aperture2. Compute plane wave amplitude (FFT)3. Perform plane wave expansion (FFT)

),( rs

),( sA

Sensor system aperture

Backpropagated wavefieldImage

rssssr ikeTAdI ),(),(),(

704/19/23

Backpropagation--the Acoustic Lens

Sensor system

Backpropagated wavefieldScattered wavefield

Object Image

),'(),'(),'('),( 3 rrrrr hOrd inI),'(),'(),'('),( 3 rrrrr hOrd inI

Single experiment generates image of the product O in( ' , ) ( ' , )r r

804/19/23

The backpropagation Algorithm

Sensor system aperture

Scattered wavefieldObject

rsssr ikeAds ),(),(

Sensor system aperture

Backpropagated wavefieldImage

rssssr ikeTAdI ),(),(),(

T P eikW

P

( ) ( , ) ( , )

( , )

s, s s

s

s

pupil function

W( , ) wave aberration function

904/19/23

The backpropagation Point Spread Function

Point spread function is the image of a point (delta function) scattererPoint spread function is the image of a point (delta function) scatterer

W ( , )s Wave aberration function models sensor and computational inaccuracies

1

4eik | ' |

| ' |

r r

r r

spherical wave Sensor system aperture

)'(),(),'( rrsssrr

ikeikWedh

backpropagated spherical wave

1004/19/23

Point Spread Function

RsssR

ikeikWedh ),(),(

Ideal Case :

= 4steradiansZero aberration and

hkR

kRkR( , ) ( )R

sinsinc

Point spread function Coherent transfer function

1104/19/23

Improving Image Qualityconfocal Ultrasound Imaging

source array detector array High quality image

Focus-on-transmit and focus-on-receiveFocus-on-transmit and focus-on-receive

),'(),'(*),'('),( 03 rrrrrr hhOrdI

Confocal mode: r=r0

2

03

0 ),'(),'('),( rrrr hOrdI

2

03

0 ),'(),'('),( rrrr hOrdI

1204/19/23

Plane wave insonification Diffraction tomography

230

00 ),'(),'(');,(),( rrrsr

rssr

hOrdik

ed II

230

00 ),'(),'(');,(),( rrrsr

rssr

hOrdik

ed II

source array detector array Partial image

),'('

),'(');,( 030 rr

rsrsr h

ikeOrdI

)'(),'(* 0

0

rrssrr

ikedh

I ( , ; )r s0

1304/19/23

Image Quality

22

23

)sin(),(

),'(),'('),(

kR

kRh

hOrdI

R

rrrr

Point spread function Transfer function

1404/19/23

Image Processing

KHkKK

H

kR

kRh

)(2for1

)(

)sin(),(

1

22

KK

R

),'(),'('),(),(ˆ

),'(),'('),(

31

23

rrrrr

rrrr

OrdHO

hOrd

I

I

•Image processing performed directly on 3D image in confocal system•Image processing performed on raw data in diffraction tomography (yields filtered backpropagation algorithm)

•Image processing performed directly on 3D image in confocal system•Image processing performed on raw data in diffraction tomography (yields filtered backpropagation algorithm)

1504/19/23

Summary and Conclusions

Single experiment ultrasound imaging of 3D objects yields extremely low image quality

Multiple experiments via confocal scanning or diffraction tomography yields high image quality

Post image processing and algorithm optimization can improve image quality

Born approximation not adequate for strong scattering and/or extended objects

Conventional (optical) measures of image quality not appropriate for 3D ultrasound