Estimation of vector velocity

• US 6,859,659 B1
• Filed: 05/10/2000
• Issued: 02/22/2005
• Est. Priority Date: 05/10/1999
• Status: Expired due to Term

• Current Assignee: B-K Medical A/S (B.K. Holding ApS)
• Original Assignee: B-K Medical A/S (B.K. Holding ApS)
• Inventors: Jensen, Jørgen Arendt
• Primary Examiner(s): Jaworski, Francis J.
• Application Number:
  US09/959,883
• Time in Patent Office: 1,749 Days
• Field of Search: 600/407, 600/437, 600/443, 600/447, 600453-456, 738/612.5, 738/612.7, 738/613.1, 367/89, 367/100, 367/125, 367/90, 250/201.9, 340/936, 340/951, 340/953, 340/957, 356/121, 342104-105, 342107-108, 342/117
• US Class Current: 600/407
• CPC Class Codes: A61B 8/06 Measuring blood flow measuring volume flow in general G01F, e.g. G01F1/66, G01F1/72; measuring speed of fluids in general G01P5/00
• CPC Class Codes: A61B 8/13 Tomography A61B8/10, A61B8/12 take precedence; tomography for radiation diagnosis A61B6/02
• CPC Class Codes: G01N 2291/02836 Flow rate, liquid level
• CPC Class Codes: G01P 13/02 Indicating direction only, e.g. by weather vane
• CPC Class Codes: G01P 5/22 using auto-correlation or cross-correlation detection means
• CPC Class Codes: G01P 5/244 involving pulsed waves
• CPC Class Codes: G01S 15/8984 Measuring the velocity vector

Abstract

A method and apparatus are provided for estimating the velocity vector of a remotely sensed object or group of objects using either ultrasound or electromagnetic radiation. The movement of the object is determined by emitting and receiving a pulsed field with spatial oscillations in both the axial and transverse directions. Using a number of pulsed emissions and the transverse spatial oscillations the received signal is influenced by transverse motion and a new autocorrelation estimator is used for determining the velocity vector.

Claims

1. An apparatus for measuring the velocity of a moving object or a collection of moving objects, the apparatus comprising:

a generator for generating pulses of excitation signals, an emitting transducer for transforming said excitation signals into a beam of wave energy and for emitting said wave energy in a predetermined direction of propagation, a receiving transducer for receiving signals from said moving object or objects generated by interaction with said wave energy emitted from said emitting transducer, wherein said emitting transducer and said receiving transducer having respective sensitivities which in combination give a resulting sensitivity oscillating spatially in a direction transverse to said direction of propagation, wherein the velocity component transverse to the beam is estimated using $\begin{array}{cc}{v}_x=\frac{d_x}{2<br><br>\mathrm{\pi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{k2T}}_{\mathrm{prf}}}<br><br>\arctan <br><br>\left(\frac{\mathrm{??}<br><br>\left\{R_1<br><br>\left(k\right)\right\}<br><br>\mathrm{ℛ<br><br>}<br><br>\left\{R_2<br><br>\left(k\right)\right\}+\mathrm{??}<br><br>\left\{R_2<br><br>\left(k\right)\right\}<br><br>\mathrm{ℛ<br><br>}<br><br>\left\{R_1<br><br>\left(k\right)\right\}}{\mathrm{ℛ<br><br>}<br><br>\left\{R_1<br><br>\left(k\right)\right\}<br><br>\mathrm{ℛ<br><br>}<br><br>\left\{R_2<br><br>\left(k\right)\right\}-\mathrm{??}<br><br>\left\{R_1<br><br>\left(k\right)\right\}<br><br>\mathrm{??}<br><br>\left\{R_2<br><br>\left(k\right)\right\}}\right)& \left(36\right)\end{array}$

 

as an estimator,

and the axial velocity component along the beam is estimated using $\begin{array}{cc}{v}_z=\frac{c}{2<br><br>\mathrm{\pi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{k4T}}_{\mathrm{prf}}<br><br>f_0}<br><br>\arctan <br><br>\left(\frac{\mathrm{??}<br><br>\left\{R_1<br><br>\left(k\right)\right\}<br><br>\mathrm{ℛ<br><br>}<br><br>\left\{R_2<br><br>\left(k\right)\right\}-\mathrm{??}<br><br>\left\{R_2<br><br>\left(k\right)\right\}<br><br>\mathrm{ℛ<br><br>}<br><br>\left\{R_1<br><br>\left(k\right)\right\}}{\mathrm{ℛ<br><br>}<br><br>\left\{R_1<br><br>\left(k\right)\right\}<br><br>\mathrm{ℛ<br><br>}<br><br>\left\{R_2<br><br>\left(k\right)\right\}+\mathrm{??}<br><br>\left\{R_1<br><br>\left(k\right)\right\}<br><br>\mathrm{??}<br><br>\left\{R_2<br><br>\left(k\right)\right\}}\right)& \left(37\right)\end{array}$

 

as an estimator,

where ℑ

{R(k)} denotes the imaginary part of the complex autocorrelation and ℑ

{R(k)} the real part, and where R₁(k) is the complex lag k autocorrelation value for the signal r₁(i) given by

r₁(i)=r_sq(i)+jr_sqh(i) 

 

(38)

 

where r_sq(i) is the received and sampled spatial quadrature field and r_sqh(i) is the spatial Hilbert transform of r_sq(i) and R₂(1) is the complex lag one autocorrelation value for the signal r₂(i) given by

r₂(i)=r_sq(i)−

jr_sqh(i), 

 

(39)

 

where i denotes the pulse-echo line number, c is the speed of the wave energy, f₀ is the center frequency of the emitted wave energy, d_x is a period of the lateral oscillation of the sensitivity, and T_prf is the time between pulse emissions.

2. An apparatus according to claim 1 where a lag greater than one is used in the estimators.

3. An apparatus according to claim 1 where the received and sampled signal is summed as $\begin{array}{c}\hat{R}\end{array}$

(k)=1(N-k)⁢

Np⁢

∑

i=0N-k⁢

∑

n=-Np/2Np/2-1⁢

r*⁡

(i,n+N0)⁢

r⁡

(i+k,n+N0)(40)

where r(i,n) denotes the signal for the i'"'"'th line and its n'"'"'th sample, N₀ is the sample number for the position of the velocity estimation, and N_p is the number of samples in a segment.

4. An apparatus according to claim 1 where the center frequency is estimated using $\begin{array}{c}{\stackrel{\_}{f}}_0\end{array}$

(z)=∫

-fs/2fs/2⁢

fPrf⁡

(f,z)⁢

ⅆ

f∫

-fs/2fs/2⁢

Prf⁡

(f,z)⁢

ⅆ

f(41)

as an estimator, where f_s is the sampling frequency, z is the depth of interest, P_n(f,z) is the spectrum of the received signal around the depth z and f is the temporal frequency.

5. An apparatus according to claim 1 where the axial velocity component is compensated for by using $\begin{array}{c}\hat{R}\end{array}$

(k)=1(N-k)⁢

Np⁢

∑

i=0N-k⁢

∑

n=-Np/2Np/2-1⁢

r*⁡

(i,n+N0-ns/2)⁢

r⁡

(i+k,n+N0+ns/2)(42)

where n_s is the axial movement compensation delay given by $\begin{array}{cc}{n}_s=\mathrm{round}<br><br>\left(k<br><br>\frac{2<br><br>v_z}{c}<br><br>T_{\mathrm{prf}}<br><br>f_s\right)& \left(43\right)\end{array}$

for the calculation of the autocorrelation.

6. An apparatus according to claim 1 where the transverse, modulation frequency used in the velocity estimator is found according to $\begin{array}{c}{\stackrel{\_}{f}}_{\mathrm{space}}=\frac{{\int }_{}^{}}{}\end{array}$

-fs/2+fs/2⁢

∫

-fsx/2+fsx/2⁢

fspace⁢



H⁡

(ftime,fspace)

2⁢

ⅆ

ftime⁢

ⅆ

fspace∫

-fs/2+fs/2⁢

∫

-fsx/2+fsx/2⁢



H⁡

(ftime,fspace)

2⁢

ⅆ

ftime⁢

ⅆ

fspace(44)

where f_sx is the lateral spatial sampling frequency and H(f_time, f_space) is the spatio-temporal Fourier transform of the complex excitation signals.

7. A method of estimating the velocity of a moving object or a collection of moving objects, the method comprising

emitting an excitation signal of pulses of wave energy as a beam in a predetermined direction of propagation, whereby at least part of the wave energy will interact with the moving object or collection of moving objects, receiving, from said moving object or objects, reflected signals resulting from interaction of emitted wave energy with the moving object or collection of moving objects, wherein the emission of the excitation signal and the reception of reflected signals have respective sensitivities which in combination give a resulting sensitivity oscillating spatially in a direction transverse to the direction of propagation, estimating the velocity component transverse to the predetermined direction, using $\begin{array}{c}{v}_x=\frac{d_x}{2}\end{array}$

π

⁢

 

⁢

k2Tprf⁢

arctan⁡

(??⁢

{R1⁡

(k)}⁢

ℛ

⁢

{R2⁡

(k)}+??⁢

{R2⁡

(k)}⁢

ℛ

⁢

{R1⁡

(k)}ℛ

⁢

{R1⁡

(k)}⁢

ℛ

⁢

{R2⁡

(k)}-??⁢

{R1⁡

(k)}⁢

??⁢

{R2⁡

(k)})(36)

 

as an estimator, and

estimating the axial velocity component along the predetermined direction using $\begin{array}{cc}{v}_z=\frac{c}{2<br><br>\mathrm{\pi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{k4T}}_{\mathrm{prf}}<br><br>f_0}<br><br>\arctan <br><br>\left(\frac{\mathrm{??}<br><br>\left\{R_1<br><br>\left(k\right)\right\}<br><br>\mathrm{ℛ<br><br>}<br><br>\left\{R_2<br><br>\left(k\right)\right\}-\mathrm{??}<br><br>\left\{R_2<br><br>\left(k\right)\right\}<br><br>\mathrm{ℛ<br><br>}<br><br>\left\{R_1<br><br>\left(k\right)\right\}}{\mathrm{ℛ<br><br>}<br><br>\left\{R_1<br><br>\left(k\right)\right\}<br><br>\mathrm{ℛ<br><br>}<br><br>\left\{R_2<br><br>\left(k\right)\right\}+\mathrm{??}<br><br>\left\{R_1<br><br>\left(k\right)\right\}<br><br>\mathrm{??}<br><br>\left\{R_2<br><br>\left(k\right)\right\}}\right)& \left(37\right)\end{array}$

 

as an estimator,

where ℑ

{R(k)} denotes the imaginary part of the complex autocorrelation and {R(k)} the real part, and where R₁(k) is the complex lag k autocorrelation value for the signal r₁(i) given by

r₁(i)=r_sq(l)+jr_sqh(i) 

 

(38)

 

where r_sq(i) is the received and sampled spatial quadrature field and r_sqh(i) is the spatial Hilbert transform of r_sq(i) and R₂(1) is the complex lag one autocorrelation value for the signal r₂(i) given by

r₂(i)=rsq(i)−

jr_sqh(i), 

 

(39)

 

where i denotes the pulse-echo line number, c is the speed of the wave energy, f₀ is the center frequency of the emitted wave energy, d_x is a period of the lateral oscillation of the sensitivity, and T_prf is the time between pulse emissions.

8. A method according to claim 7 where the received and sampled signal is summed as $\begin{array}{c}\hat{R}\end{array}$

(k)=1(N-k)⁢

Np⁢

∑

i=0N-k⁢

∑

n=-Np/2Np/2-1⁢

r*⁡

(i,n+N0)⁢

r⁡

(i+k,n+N0)(40)

where r(i,n) denotes the signal for the i'"'"'th line and its n'"'"'th sample, N₀ is the sample number for the position of the velocity estimation, and N_p is the number of samples in a segment.

9. A method according to claim 7 where the center frequency is estimated using $\begin{array}{c}{\stackrel{\_}{f}}_0\end{array}$

(z)=∫

-fs/2fs/2⁢

fPrf⁡

(f,z)⁢

ⅆ

f∫

-fs/2fs/2⁢

Prf⁡

(f,z)⁢

ⅆ

f(41)

as an estimator, where f_s is the sampling frequency, z is the depth of interest, P_r(f,z) is the spectrum of the received signal around the depth z and f is the temporal frequency.

10. A method according to claim 7 where the axial velocity component is compensated for by using $\begin{array}{c}\hat{R}\end{array}$

(k)=1(N-k)⁢

Np⁢

∑

i=0N-k⁢

∑

n=-Np/2Np/2-1⁢

r*⁡

(i,n+N0-ns/2)⁢

r⁡

(i+k,n+N0+ns/2)(42)

where n_s is the axial movement compensation delay given by $\begin{array}{cc}{n}_s=\mathrm{round}<br><br>\left(k<br><br>\frac{2<br><br>v_z}{c}<br><br>T_{\mathrm{prf}}<br><br>f_s\right)& \left(43\right)\end{array}$

for the calculation of the autocorrelation.

11. A method according to claim 7 where the transverse modulation frequency used in the velocity estimator is found according to $\begin{array}{c}{\stackrel{\_}{f}}_{\mathrm{space}}=\frac{{\int }_{}^{}}{}\end{array}$

-fs/2+fs/2⁢

∫

-fsx/2+fsx/2⁢

fspace⁢



H⁡

(ftime,fspace)

2⁢

ⅆ

ftime⁢

ⅆ

fspace∫

-fs/2+fs/2⁢

∫

-fsx/2+fsx/2⁢



H⁡

(ftime,fspace)

2⁢

ⅆ

ftime⁢

ⅆ

fspace(44)

where f_sx is the lateral spatial sampling frequency and H(f_time, f_space) is the spatio-temporal Fourier transform of the complex excitation signal.