# Three-dimensional quantitative ultrasound imaging by smapdi62

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```									               Three-dimensional Quantitative
Ultrasound Imaging
Devaney@ece.neu.edu       Tonydev2@aol.com

A.J. Devaney
Department of electrical and computer engineering
Northeastern university
Boston, MA 02115

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

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

1/13/2010                                                                        1
Canonical Imaging Configuration
Sensor system

Insonifying waveform

Scattered wavefield

(  2  k 2 )  ( r ,  )  O( r ,  )  ( r ,  )
O( r ,  )  k 2 [1  n 2 ( r ,  )]

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

1/13/2010                                                                              2
Data Model
 (r ,  )   in (r,  )   s (r ,  )
ik | r  r '|
e
 s (r,  )   41  d 3 r ' O(r' ,  ) (r ' ,  )
| r  r '|
• Nonlinear and nonlocal mapping from object function to scattered field
• Mapping from 3D to 2D thus non-unique

Born approximation
Rytov approximation

ik | r  r '|
e
 b (r,  )   41  d 3 r ' O(r' ,  ) in (r ' ,  )
s

| r  r '|

1/13/2010                                                                                      3
Born Approximation Imaging
ik| r  r ' |
e
 bs (r,  )   41  d 3r 'O(r ' ,  ) in (r ' ,  )
| r  r'|

“Lens”
outgoing spherical wave                         Incoming spherical wave

scattering point    .                                                               Image point

ik | r  r '|
1 e
                     h ( r  r ',  )
4  | r  r '|

 bs (r,  )   I (r,  )   d 3r 'O(r' ,  ) in (r' ,  )h(r  r' ,  )

1/13/2010                                                                                               4
Analog Two-dimensional
Imaging             x,y
x,y

Object                     Lens                      Image

I ( x , y )   dx ' dy ' h( x  x ' , y  y ' ) I ( x ' , y ' )


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

1/13/2010                                                                      5
Backpropagation Imaging
Scattered wavefield
Object
Sensor system aperture
 (r,  )   ds A(s,  )eiks  r
s


1.   Measure wavefield  (r,  ) over aperture
s

2.   Compute plane wave amplitude A(s,  ) (FFT)
3.   Perform plane wave expansion (FFT)

Backpropagated wavefield
Image
Sensor system aperture
 I (r,  )   ds A(s,  )T (s,  )eiks  r   

1/13/2010                                                                                                         6
Backpropagation--the Acoustic
Lens

Sensor system

Object                                                                                         Image

Scattered wavefield                                                          Backpropagated wavefield

 I (r,  )   d 3r 'O(r' ,  ) in (r' ,  )h(r  r' ,  )

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

1/13/2010                                                                                              7
The backpropagation Algorithm
Scattered wavefield
Object
Sensor system aperture
 (r,  )   ds A(s,  )eiks  r
s


T ( s,  )  P ( s ,  ) eikW ( s ,  )
P ( s ,  )  pupil function
W( s ,  )  wave aberration function

Image                      Backpropagated wavefield

Sensor system aperture
 I (r,  )   ds A(s,  )T (s,  )eiks  r   

1/13/2010                                                                                                           8
The backpropagation Point

spherical wave       Sensor system aperture                backpropagated spherical wave

ik | r  r '|                                                       ikW (s, ) iks  (r  r ' )

1 e                                         h(r  r ' ,  )   ds e             e                            
4  | r  r '|                                                 

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

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

1/13/2010                                                                                                             9
Ideal Case :
ikW (s,  ) iks  R       Zero aberration and  = 4steradians
h(R,  )   ds e              e


       h( R ,  ) 
sin kR
 sinc ( kR )
kR

Point spread function                     Coherent transfer function

1/13/2010                                                                               10
Improving Image Quality
confocal Ultrasound Imaging

source array                     detector array                         High quality image

 I (r,  )   d 3r 'O(r' ,  ) h * (r0  r' ,  )h(r  r' ,  )
Confocal mode: r=r0

 I (r0 ,  )   d 3r 'O(r' ,  ) h(r0  r' ,  )
2

1/13/2010                                                                                          11
Plane wave insonification
Diffraction tomography
source array                            detector array                                 Partial image

 I ( r , ; s 0 )

iks 0  r '
 I (r,  ; s 0 )   d 3 r 'O(r ' ,  ) e                       h(r  r ' ,  )
iks 0  (r 'r )
h * (r  r ' ,  )   ds 0 e


 iks 0  r
 I (r,  )   ds 0 e                I (r,  ; s 0 )   d 3 r 'O(r ' ,  ) h(r  r ' ,  )
2



1/13/2010                                                                                                               12
Image Quality

 I (r,  )   d r 'O(r ' ,  ) h(r  r ' ,  )
3                                2

2
 sin(kR) 
h( R ,  )  
2

 kR 

1/13/2010                                                                        13
Image Processing
2
 sin(kR) 
h( R ,  )  
2

 kR 
1
H (K )    for K  2k  H 1 (K )  K
K

 I (r,  )   d r 'O(r ' ,  ) h(r  r ' ,  )
3                               2

ˆ
O(r,  )  H 1  I (r,  )   d 3r 'O(r ' ,  )(r  r ' ,  )

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

1/13/2010                                                                           14
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

1/13/2010                                                       15

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