Time reversal and phase coherent music techniques for super-resolution ultrasound imaging
View Patent ↗Systems and methods for super-resolution ultrasound imaging using a windowed and generalized TR-MUSIC algorithm that divides the imaging region into overlapping sub-regions and applies the TR-MUSIC algorithm to the windowed backscattered ultrasound signals corresponding to each sub-region. The algorithm is also structured to account for the ultrasound attenuation in the medium and the finite-size effects of ultrasound transducer elements. A modified TR-MUSIC imaging algorithm is used to account for ultrasound scattering from both density and compressibility contrasts. The phase response of ultrasound transducer elements is accounted for in a PC-MUSIC system.
1. A method of performing ultrasound imaging of a medium, the method comprising:
exciting a first transducer element in an array of transducer elements to direct an ultrasound signal into a target region of the medium;
receiving a backscatter signal from the target region within the medium from the array of transducer elements;
generating an inter-element transfer matrix of the received backscatter signal;
said inter-element transfer matrix comprising density contrast data relating to one or more scatterers within said medium;
generating a generalized time-reversal (TR) matrix from the inter-element transfer matrix; and
generating a pseudo-spectrum for generalized TR-Music imaging of the target region,
said pseudo-spectrum comprising density contrast data relating to one or more scatterers within said medium,
wherein generating the inter-element transfer matrix comprises calculating the inter-element transfer matrix as a function of an electro-mechanical response of each transducer element in the array, a diffraction response of each transducer element in the array, and attenuation in the target region.
2. A method as recited in claim 1 :
wherein said inter-element transfer matrix further comprises compressibility contrast data; and
wherein said pseudo-spectrum comprises density contrast data and compressibility contrast data relating to one or more scatterers within said medium.
3. A method as recited in claim 2 , further comprising obtaining said density contrast data and compressibility contrast data from least squares estimation of a pseudo-spectrum generated from TR-MUSIC imaging.
4. A method as recited in claim 2 , wherein said inter-element transfer matrix K is calculated according to the function:
K
=
F
(
ω
)
∑
m
=
1
M
γ
κ
(
r
m
)
A
(
r
m
)
A
T
(
r
m
)
+
γ
ρ
(
r
m
)
[
B
1
(
r
m
)
B
2
(
r
m
)
…
B
N
(
r
m
)
]
where F(ω) is a electromechanical transfer function, M is the number of the scatterers within said medium, r m is a location of an m th point scatter, γ ρ is the density contrast, γ κ , is the compressibility contrast, and superscript T denotes the transpose of the vector, A(r m ) is a vector given by:
A T ( r m )=[ a 1 ( r m ) a 2 ( r m ) . . . a N ( r m )], B n ( r m )
is a vector given by:
B n T ( r m )=[cos(θ m 1,n ) a 1 ( r m ) a n ( r m )cos(θ m 2,n ) a 2 ( r m ) a n ( r m ) . . . cos(θ m N,n ) a N ( r m ) a n ( r m )],
a i is the integral of Green's function over the surface element i, i is 1 to N, and θ m i ,n is the angle between a vector from the center of the transmitting element to a point where an inhomogeneity is located.
5. A method as recited in claim 4 , wherein the pseudo-spectrum φ(r) is calculated according to the equation:
Φ
(
r
)
=
1
∑
σ
p
=
0
u
p
†
A
(
r
)
2
+
1
∑
σ
p
=
0
∑
n
=
1
N
u
p
†
B
n
(
r
)
2
where superscript † denotes the transpose of the complex conjugate of a vector or a matrix, 94 p , are singular values, and μ p is a left singular vector.
6. A method as recited in claim 1 , wherein the diffraction response of each transducer element is a function of finite size effects of the array of transducer elements.
7. A method as recited in claim 1 , wherein the step of receiving backscatter signal comprises:
dividing an imaging plane of the target region into a plurality of sub-regions;
imaging each sub-region in the plurality of sub-regions separately; and
combining each sub-region to form an entire image of the target region.
8. An ultrasound imaging system for imaging of a medium, the system comprising:
(a) a processor; and
(b) programming executable on said processor for:
(i) exciting a first transducer element in an array of transducer elements to direct an ultrasound signal into a target region of the medium;
(ii) receiving a backscatter signal from the target region within the medium from the array of transducer elements;
(iii) generating an inter-element transfer matrix of the received backscatter signal;
(iv) said inter-element transfer matrix comprising density contrast data relating to one or more scatterers within said medium;
(v) generating a generalized time-reversal (TR) matrix from the inter-element transfer matrix; and
(vi) generating a pseudo-spectrum for generalized TR-Music imaging of the target region,
said pseudo-spectrum comprising density contrast data relating to one or more scatterers within said medium,
wherein generating the inter-element transfer matrix comprises calculating the inter-element transfer matrix as a function of an electro-mechanical response of each transducer element in the array, a diffraction response of each transducer element in the array, and attenuation in the target region.
9. A system as recited in claim 8 : wherein said inter-element transfer matrix further comprises compressibility contrast data; and wherein said pseudo-spectrum comprises density contrast data and compressibility contrast data relating to one or more scatterers within said medium.
10. A system as recited in claim 9 , wherein the density contrast data and compressibility contrast data are obtained from least squares estimation of a pseudo-spectrum generated from TR-MUSIC imaging.
11. A system as recited in claim 9 , wherein said inter-element transfer matrix K is calculated according to the function:
K
=
F
(
ω
)
∑
m
=
1
M
γ
κ
(
r
m
)
A
(
r
m
)
A
T
(
r
m
)
+
γ
ρ
(
r
m
)
[
B
1
(
r
m
)
B
2
(
r
m
)
…
B
N
(
r
m
)
]
where F(ω) is a electromechanical transfer function, M is the number of the scatterers within said medium, r m is a location of an m th point scatter, γ ρ is the density contrast, γ κ is the compressibility contrast, and superscript T denotes the transpose of the vector, where A(r m ) is a vector given by:
A T ( r m )=[ a 1 ( r m ) a 2 (r m ) . . . a N ( r m )],
and where B n (r m ) is a vector given by:
B n T ( r m )=[cos(θ m 1,n ) a 1 ( r m ) a n ( r m )cos(θ m 2,n ) a 2 ( r m ) a n ( r m ) . . . cos(θ m N,n ) a N ( r m ) a n ( r m )],
a I is the integral of Green's function over the surface element i, i is 1 to N, and θ m i ,n is the angle between a vector from the center of the transmitting element to a point where an inhomogeneity is located.
12. A system as recited in claim 11 , wherein the pseudo-spectrum is calculated according to the equation:
Φ
(
r
)
=
1
∑
σ
p
=
0
u
p
†
A
(
r
)
2
+
1
∑
σ
p
=
0
∑
n
=
1
N
u
p
†
B
n
(
r
)
2
wherein superscript † denotes the transpose of the complex conjugate of a vector or a matrix, σ p , are singular values, and μ p is a left singular vector.
13. A system as recited in claim 8 , wherein the diffraction response of each transducer element is a function of the finite size effects of the array of transducer elements.
14. A system as recited in claim 8 , wherein the step of receiving the backscatter signal comprises:
dividing an imaging plane of the target region into a plurality of sub-regions;
imaging each sub-region in the plurality of sub-regions separately; and
combining each sub-region to form an entire image of the target region.