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


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                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 '|



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                   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' ,  )


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             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.


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                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   




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                            The backpropagation Point
                            Spread Function

                       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
                       Point Spread Function
                                              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




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               Improving Image Quality
               confocal Ultrasound Imaging
                      Focus-on-transmit and focus-on-receive


      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 


            Point spread function                            Transfer function




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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