1. Ultrasonic reflectivity imaging with a depth extrapolation algorithm Ernesto Bonomi, Giovanni Cardone, Enrico Pieroni CRS4, Italy

2. STROBL 20002Ultrasound Imaging Prerequisites Inverse obstacle problem unknown object model: assembly of scatterers in a constant velocity background medium (c=1540 m/s) Scatterer sharp discontinuity of the medium Resulting reconstruction image: map of the medium reflectivity Constraint: real-time processing

3. STROBL 20003Ultrasound Imaging Offset acquisition geometry Transmission: 128 syncronous shooting elements Virtual source Circular wavefront Reception: 128 recording elements echoes from the entire domain scatterer 2 scatterer 1 TIME RECEIVER 64: PROBE CURVATURE CENTER PROBE SURFACE EMITTED WAVEFRONT VIRTUAL SOURCE ECHOS RECEIVER 64 SCATTERER 2 SCATTERER 1

4. STROBL 20004Ultrasound Imaging  Wave equation in polar coordinates  Fourier sum over time and angle: Bessel equation  Behavior of the two solutions (Hankel functions) Propagation

5. STROBL 20005Ultrasound Imaging Depth extrapolation 1  Hankel functions:  the region of interest allows neither the use of series ( )  nor asymptotic expansions ( )  Depth extrapolation from to :  for instance, backward in time: cumbersome problem

6. STROBL 20006Ultrasound Imaging Depth extrapolation 2  is slowly variable within when  Solve the approximated Bessel equation:  Polar Phase Shift (PPS) where  The plus sign: propagation backward in time  A similar approach is used in seismic data migration:  in cartesian coordinates, Phase Shift formula, exact for  constant velocity media

7. STROBL 20007Ultrasound Imaging Imaging condition Reflection point: the downward propagation of the source (forward in time) and of the recorded echo (backward in time) are coincident at the same moment: zero lag correlation

8. STROBL 20008Ultrasound Imaging Operators comparison 1 Error norm

9. STROBL 20009Ultrasound Imaging Operators comparison 2 Angle error norm Amplitude error norm

10. STROBL 200010Ultrasound Imaging Operators comparison 3 Amplitude error Angle error

11. STROBL 200011Ultrasound Imaging Operators comparison 4 Amplitude error Angle error

12. STROBL 200012Ultrasound Imaging Operators comparison 5 Amplitude error Angle error

13. STROBL 200013Ultrasound Imaging Operators comparison 6 Amplitude error Angle error

14. STROBL 200014Ultrasound Imaging Full extrapolation 1 Angle error/pi

15. STROBL 200015Ultrasound Imaging Full extrapolation 2 Amplitude error

16. STROBL 200016Ultrasound Imaging Standard versus OPPS  STANDARD:  an acoustic beam scans the region of interest to compose the image.  The number of shots usually equals the number of probe elements (128~256).  Single focusing in transmission and dynamical in reception Source/receivers (moving aperture) probe Beam focused along each view line  OPPS:  one shot with all elements, no transmission focusing, thus allowing higher frame rate (~3000 frs vs ~30 frs).  The reconstruction method is ‘closer’ to the acoustic propagation physics, achieving a better quality at the same conditions

17. STROBL 200017Ultrasound Imaging A ‘real’ case Phantom model Recorded data spectrum Evanescent region

18. STROBL 200018Ultrasound Imaging Reconstruction OPPS Standard Non uniform image quality Lower contrast

19. STROBL 200019Ultrasound Imaging Reconstruction error exact - OPPS Normalized image

20. STROBL 200020Ultrasound Imaging Resolution standard: tx+rx focusing OPPS standard: rx focusing only

21. STROBL 200021Ultrasound Imaging Resolution bis standard: tx+rx focusing OPPS standard: rx focusing only