Windowed time-reversal music technique 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.
1. A method of performing ultrasound imaging of a medium, comprising:
exciting a first transducer element in an array of transducer elements to direct an ultrasound signal into a target region within the medium;
receiving a backscatter signal from the target region within the medium with the array of transducer elements;
generating an inter-element transfer matrix of the received backscatter signal;
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,
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 the diffraction response of each transducer element is a function of finite size effects of the array of transducer elements.
3. A method as recited in claim 2 ,
wherein the inter-element transfer matrix is calculated as according to a function a i (r 0 ,ω) over a surface of a transducer element i,
wherein:
a
i
(
r
0
,
ω
)
=
∫
∫
S
i
g
0
(
r
❘
r
0
)
d
s
,
and
wherein ω is an angular frequency, ds is a delimiter of integration, g 0 (ω,r|r 0 ) is the free-space Green's function, a i (r 0 ,ω) is the integral of the Green's function over the surface of element i, and r corresponds to a location of a wavefield resulting from a point source at a location r 0 .
4. A method as recited in claim 1 ,
wherein the inter-element transfer matrix K is calculated according to the function:
K
=
2
i
k
_
4
ω
κ
0
F
(
ω
)
∫
∫
∫
V
0
γ
κ
(
r
0
)
A
r
0
A
r
0
T
d
v
0
;
and
wherein i is an imaginary unit, k is a complex wave number, ω is an angular frequency, κ 0 is an average compressibility of the medium, F(ω) is an electromechanical transfer function, V 0 is a scattering volume, γ κ is a fluctuation equation, r 0 is a location, dv 0 is a delimiter of integration, and the superscript T in A r a T denotes that A r 0 T is the transpose of A r 0 which is an N-dimensional column vector given by:
[ a 1 ( r 0 ,ω) a 2 ( r 0 ,ω) . . . a N ( r 0 ,ω)].
5. A method as recited in claim 1 ,
wherein the generalized time-reversal matrix is calculated according to:
T
=
-
4
k
_
8
(
ω
κ
0
)
2
F
(
ω
)
2
∑
m
=
1
M
∑
m
′
=
1
M
Λ
m
,
m
′
A
r
m
*
A
r
m
′
T
,
wherein
:
A
r
m
T
=
[
a
1
(
r
m
,
ω
)
a
2
(
r
m
,
ω
)
…
,
a
N
(
r
m
,
ω
)
]
;
and
Λ
m
,
m
′
=
γ
κ
(
r
m
)
γ
κ
(
r
m
′
)
〈
A
r
m
,
A
r
m
′
〉
,
and
wherein i is an imaginary unit, k is a complex wave number, ω is an angular frequency, κ 0 is an average compressibility of the medium, F(ω) is an electromechanical transfer function, m and m′ are variables which range from 1 to M, M the number of scatterers, A* r m corresponds to vectors associated with the scatterers, and A r′ m T is the transpose of A r′ m .
6. A method as recited in claim 5 ,
wherein the pseudo-spectrum PS(r) is calculated according to the equation:
PS
(
r
)
=
1
∑
m
0
=
M
+
1
N
〈
μ
m
0
*
,
Λ
r
〉
2
,
and
wherein M corresponds to a number of scatterers in the target region, N corresponds to the number transducer elements in the array, μ* m 0 is the complex-conjugate of μ m 0 which corresponds to an eigenvector with a zero eigenvalue, and A r corresponds to vectors associated with r which corresponds to a location of a wavefield resulting from a point source at a location r 0 .
7. A method as recited in claim 1 ,
wherein the inter-element transfer matrix is calculated as according to a function g 0 (ω,r|r 0 ),
wherein:
g
0
(
ω
,
r
❘
r
0
)
=
exp
-
i
k
_
r
-
r
0
4
π
r
-
r
0
;
and
k
_
=
ω
c
-
i
α
,
and
wherein k is a complex wave number, r corresponds to a location of a wavefield resulting from a point source at a location r 0 , exp( ) is Euler's number raised to the power of the quantity in the parenthesis, k=ω/c is a real wave number, ω is angular frequency, α is the amplitude attenuation coefficient, c is the average sound speed, and i is the imaginary unit.
8. An ultrasound imaging 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 tissue;
(ii) receiving a backscatter signal from the target region with the array of transducer elements; and
(iii) performing time reversal imaging by:
generating an inter-element transfer matrix of the received backscatter signal;
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,
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 finite size effects of the array of transducer elements are factored in calculating the inter-element response matrix.
10. A system as recited in claim 8 ,
wherein the inter-element transfer matrix K is calculated according to the equation:
K
=
2
i
k
4
ω
κ
0
F
(
ω
)
∫
∫
∫
V
0
γ
κ
(
r
0
)
A
r
0
A
r
0
T
d
v
0
,
and
wherein i is an imaginary unit, k is a complex wave number, ω is an angular frequency, κ 0 is an average compressibility of the medium, F(ω) is an electromechanical transfer function, V 0 is a scattering volume, γ κ is a fluctuation equation, r 0 is a location, dv 0 is a delimiter of integration, and the superscript T in A r 0 T denotes that A r 0 T is the transpose of A r 0 which is an N-dimensional column vector given by:
[ a 1 ( r 0 ,ω) a 2 ( r 0 ,ω) . . . a N ( r 0 ,ω)].
11. A system as recited in claim 8 ,
wherein the generalized time-reversal matrix is calculated according to:
T
=
-
4
k
_
8
(
ω
κ
0
)
2
F
(
ω
)
2
∑
m
=
1
M
∑
m
′
=
1
M
Λ
m
,
m
′
A
r
m
*
A
r
m
′
T
,
wherein
:
A
r
m
T
=
[
a
1
(
r
m
,
ω
)
a
2
(
r
m
,
ω
)
…
,
a
N
(
r
m
,
ω
)
]
;
and
Λ
m
,
m
′
=
γ
κ
(
r
m
)
γ
κ
(
r
m
′
)
〈
A
r
m
,
A
r
m
′
〉
,
and
wherein i is an imaginary unit, k is a complex wave number, ω is an angular frequency, κ 0 is an average compressibility of the medium, F(ω) is an electromechanical transfer function, m and m′ are variables which range from 1 to M, M the number of scatterers, A* r m corresponds to vectors associated with the scatterers, and A r′ m T is the transpose of A r′ m .
12. A system as recited in claim 8 ,
wherein the inter-element transfer matrix is calculated as according to a function g 0 (ω,r|r 0 ),
wherein:
g
0
(
ω
,
r
❘
r
0
)
=
exp
-
i
k
_
r
-
r
0
4
π
r
-
r
0
;
k
_
=
ω
c
-
i
α
,
and
wherein k is a complex wave number, r and r 0 are locations, exp( ) is Euler's number raised to the power of the quantity in the parenthesis, k=ω/c is the real wave number, ω is the angular frequency, α is the amplitude attenuation coefficient, c is the average sound speed, and i is the imaginary unit.
13. A system as recited in claim 8 ,
wherein the inter-element transfer matrix is calculated as according to the function a i (r 0 ,ω) over a surface of a transducer element i,
wherein:
a
i
(
r
0
,
ω
)
=
∫
∫
S
i
g
0
(
r
❘
r
0
)
d
s
,
and
wherein w is an angular frequency, ds is a delimiter of integration, is g 0 (ω,r|r 0 ) is the free-space Green's function, a i (r 0 ,ω) is the integral of the Green's function over the surface of element i, and r corresponds to a location of a wavefield resulting from a point source at a location r 0 .