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

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

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

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

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

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

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

STROBL 20008Ultrasound Imaging Operators comparison 1 Error norm

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

STROBL Ultrasound Imaging Operators comparison 3 Amplitude error Angle error

STROBL Ultrasound Imaging Operators comparison 4 Amplitude error Angle error

STROBL Ultrasound Imaging Operators comparison 5 Amplitude error Angle error

STROBL Ultrasound Imaging Operators comparison 6 Amplitude error Angle error

STROBL Ultrasound Imaging Full extrapolation 1 Angle error/pi

STROBL Ultrasound Imaging Full extrapolation 2 Amplitude error

STROBL Ultrasound 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

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

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

STROBL Ultrasound Imaging Reconstruction error exact - OPPS Normalized image

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

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