Apparatus and method for estimating a velocity of at least one scatterer in a medium
An apparatus for estimating a velocity of at least one scatterer in a medium, the apparatus including a curved array of virtual transducers (T 1 -T n ) for emitting Archimedean spiral waves in a plurality of predetermined directions of propagation defined by a set of insonification angles, and for receiving, from the at least one scatterer, scattered signals generated by scattering of the Archimedean spiral waves emitted from the curved array of virtual transducers, a driving and processing unit (U c ) for estimating the velocity of the at least one scatterer.
1. An apparatus configured to estimate a velocity of at least one scatterer in a medium, wherein the apparatus comprises:
a generator configured to generate excitation signals,
a curved array of virtual transducers configured to transform said excitation signals into Archimedean spiral waves and configured to:
emit said Archimedean spiral waves in a plurality of predetermined directions of propagation defined by a set of insonification angles α i , wherein a curvature of said curved array of virtual transducers defines a reference center and a radius of curvature r n , and to receive, from said at least one scatterer, scattered signals generated by scattering of said Archimedean spiral waves emitted from said curved array of virtual transducers,
a driving and processing unit configured to drive the generator and the curved array of virtual transducers, and configured to estimate the velocity of the at least one scatterer,
wherein axial and lateral velocity components are estimated using a set of local wavefront orientations α eq,i of the Archimedean spiral waves as a function of:
the set of insonification angles α i ,
a geometry of the curved array of virtual transducers which includes the reference center and the radius of curvature r n , and
the distance r from said at least one scatterer to the reference center, and wherein each local wavefront orientation satisfies the following formula:
α
eq
,
i
=
arcsin
(
r
n
r
sin
α
i
)
.
2. The apparatus according to claim 1 , wherein the driving and processing unit comprises a controller configured to drive the generator in order to generate at least two series of excitation signals at a constant repetition interval, and configured to drive the curved array of virtual transducers in order to transform said at least two series of excitation signals into Archimedean spiral waves, wherein:
a first series of excitation signals allows the obtaining of a first gathering of scattered signals, and
a second series of excitation signals allows the obtaining of a second gathering of scattered signals.
3. The apparatus according to claim 2 , wherein the driving and processing unit comprises a beamformer which:
receives said first and second gatherings of scattered signals generated by scattering of said Archimedean spiral waves,
delays and sums said first gathering of scattered signals in order to generate first groups of receive beams having a respective receive angle, each group of receive beams corresponding to a respective insonification angle,
delays and sums said second gathering of scattered signals in order to generate second groups of receive beams having a respective receive angle, each group of receive beams corresponding to a respective insonification angle.
4. The apparatus according to claim 3 , wherein each of the first and second groups of receive beams comprise a plurality of images, each image being associated with a respective pair of insonification angle and receive angle, and wherein the driving and processing unit further comprises a processor configured to Doppler process said first and second groups of receive beams for any given pair of images of the first and second groups of receive beams having the same pair of insonification angle and receive angle so that velocity fields are estimated for each pair of distinct spiral orientations and receive beam orientations.
5. The apparatus according to claim 4 , wherein the processor is configured to implement the following steps for each pair of images of the first and second groups of receive beams having the same pair of insonification angle and receive angle:
estimating a displacement field for each corresponding pixel between the images of a given pair of images,
estimating, from the displacement field, a doppler frequency shift per pixel for said given pair of images.
6. The apparatus according to claim 4 , wherein the processor is to implement an algebraic inversion step where several projections of the velocity field and their known orientations are used to estimate radial and azimuthal components of the velocity field.
7. The apparatus according to claim 6 , wherein the processor is configured to estimate axial and lateral velocity components from the radial and azimuthal components of the velocity field.
8. A method for estimating the velocity of at least one scatterer in a medium, wherein the method comprises:
generating of excitation signals,
transforming of said excitation signals into Archimedean spiral waves,
emitting said Archimedean spiral waves in a plurality of predetermined directions of propagation defined by a set of insonification angles, a curvature of said curved array of virtual transducers defining a reference center and a radius of curvature,
receiving scattered signals generated by scattering of said Archimedean spiral waves emitted from said curved array of virtual transducers,
estimating the velocity of the at least one scatterer,
wherein axial and lateral velocity components are estimated using a set of local wavefront orientations α eq,i of the Archimedean spiral waves as a function of:
the set of insonification angles α i ,
a geometry of the curved array of virtual transducers which includes the reference center and the radius of curvature r n , and
the distance r from said at least one scatterer to the reference center, and wherein each local wavefront orientation satisfies the following formula:
α
eq
,
i
=
arcsin
(
r
n
r
sin
α
i
)
.
9. The method according to claim 8 , wherein:
the step of generating excitation signals includes generating at least two series of excitation signals at a constant repetition interval, and
the step of transforming includes transforming said at least two series of excitation signals into Archimedean spiral waves:
a first series of excitation signals allowing the obtaining of a first gathering of scattered signals, and
a second series of excitation signals allowing the obtaining of a second gathering of scattered signals.
10. The method according to claim 9 , wherein the step of estimating the velocity of the at least one scatterer includes a beamforming substep comprising:
receiving said first and second gatherings of scattered signals generated by scattering of said Archimedean spiral waves,
delaying and summing of said first gathering of scattered signals in order to generate first groups of receive beams having a respective receive angle, each group of receive beams corresponding to a respective insonification angle, and
delaying and summing of said second gathering of scattered signals in order to generate second groups of receive beams having a respective receive angle, each group of receive beams corresponding to a respective insonification angle.
11. The method according to claim 10 , wherein each of the first and second groups of receive beams comprise a plurality of images, each image being associated with a respective pair of insonification angle and receive angle, the step of estimating the velocity of the at least one scatterer further comprising:
Doppler processing of said first and second groups of receive beams for any given pair of images of the first and second groups of receive beams having the same pair of insonification angle and receive angle so that velocity fields are estimated for each pair of distinct spiral orientations and receive beam orientations.
12. The method according to claim 10 , wherein the step of estimating the velocity of the at least one scatterer further includes the following substeps for each pair of images of the first and second groups of receive beams having the same pair of insonification angle and receive angle:
estimating of a displacement field for each corresponding pixel between the images of a given pair of images,
estimating, from the displacement field, a doppler frequency shift per pixel for said given pair of images.
13. The method according to claim 10 , wherein the step of estimating the velocity of the at least one scatterer further includes an algebraic inversion step where several projections of the velocity field and their known orientation are used to estimate radial and azimuthal components of the velocity field.
14. The method according 13 , wherein the step of estimating the velocity of the at least one scatterer further includes computing the axial and lateral velocity components from the radial and azimuthal components of the velocity field.