Ultra-dense electrode-based brain imaging system
An ultra-dense electrode-based brain imaging system with high spatial and temporal resolution. A Sparsity and Smoothness enhanced Method Of Optimized electrical TomograpHy (s-SMOOTH) based reconstruction technique to improve the spatial resolution and localization accuracy of reconstructed brain images is described. Also described is a graph Fractional-Order Total Variation (gFOTV) based reconstruction technique to improve the spatial resolution and localization accuracy of reconstructed brain images.
1. An electrode-based brain imaging system, said system comprising:
(a) an ultra-high density electrode array;
(b) a data acquisition and processing unit; and
(c) an output device;
(d) the data acquisition and processing unit comprising:
(i) a computer processor; and
(ii) a memory storing instructions executable by the computer processor;
(iii) wherein when executed by the computer processor, said instructions transform electrical signals acquired by said data acquisition and processing unit from said electrode array into a three-dimensional image by performing s-SMOOTH based reconstruction and presenting said image to said output device; and
(iv) wherein said s-SMOOTH based reconstruction comprises:
(1) defining a voxel-based total generalized variation (vTGV) on triangular mesh to enhance the smoothness of the reconstructed source;
(2) incorporating l 1-2 regularization to enhance the sparsity of reconstructed source;
(3) performing voxel-based total generalized variation (vTGV) and l 1-2 regularized EEG source reconstruction according to
min
u
1
2
||
Au
-
b
||
2
2
+
vTGV
(
α
1
,
α
2
)
2
(
u
)
+
α
3
||
u
||
1
-
2
,
β
where the first term is data fidelity term, the second term is vTGV regularization, and the third term is l 1-2 regularization; and
(4) using alternating direction method of multipliers (ADMM) according to:
Algorithm 1 s-SMOOTH EEG Reconstruction
Input the electrical measurements b, the sensing matrix A, the difference
operators D and E, the parameters α 1 , α 2 , α 3 , ρ and β, as well as the
stopping criteria of the algorithm.
Initialize the current density u and the auxiliary variables p, x, y, z, {tilde over (x)}, {tilde over (y)}, {tilde over (z)}
as zero vectors.
Iterate the algorithm to update the above variables as follows
{
u
←
(
A
T
A
+
ρ
(
D
T
D
+
I
)
)
-
1
(
A
T
b
+
ρD
T
(
p
+
x
-
x
~
)
+
ρ
(
z
-
z
~
)
)
p
←
(
E
T
E
+
I
)
-
1
(
(
Du
-
x
+
x
~
)
+
E
T
(
y
-
y
~
)
)
.
x
←
prox
α
1
/
ρ
(
Du
-
p
+
x
~
)
y
←
prox
α
2
/
ρ
(
Ep
+
y
~
)
z
←
prox
α
3
/
ρ
(
u
+
z
~
+
α
3
β
ρ
q
)
x
~
←
x
~
+
Du
-
p
-
x
y
~
←
y
~
+
Ep
-
y
z
~
←
z
~
+
u
-
z
+
α
3
β
ρ
q
where prox γ (x) = sign(x) ⊙ max{|x| − γ, 0} with componentwise
multiplication ⊙, also known as shrinkage operator.
End when the stopping criteria are met.
Output the reconstructed current density u.
2. The system of claim 1 , wherein said instructions when executed by the computer processor remove artifacts from the electrical signals by performing steps comprising:
subtracting motion artifacts in the analog domain, by using skin impedance levels as an indication of the motion artifact signal; and
estimating motion artifacts with an adaptive filter by simultaneously measuring skin impedance levels and the electrical signals;
wherein motion artifacts are canceled in the analog domain.
3. The system of claim 1 , wherein the output device comprises a visual display device.
4. The system of claim 1 , wherein together the ultra-high density electrode array and data acquisition and processing unit are configured for capturing functional brain information with high temporal and spatial resolution.
5. The system of claim 1 , wherein the ultra-high density electrode array comprises from about 64 to about 10,000 electrodes.
6. The system of claim 1 , further comprising a wireless communications interface interconnecting the electrode array and the data acquisition and processing unit.
7. The system of claim 1 , wherein said data acquisition and processing unit has a low noise input configured for acquiring said electrical signals and routing said signals to said computer processor.
8. The system of claim 1 , wherein said ultra-high density electrode array is developed using a realistic head model constructed based on high-resolution MRI from a subject.
9. The system of claim 1 , wherein said instructions when executed by said computer processor carry out a spatially focused electrode algorithm which reduces cross-talking among electrodes and improves the spatial resolution in the forward imaging by applying an optimal weighting matrix.
10. An electrode-based brain imaging system, said system comprising:
(a) an ultra-high density electrode array;
(b) a data acquisition and processing unit;
(c) a wireless communications interface interconnecting the electrode array and the data acquisition and processing unit; and
(d) a visual display device;
(e) the data acquisition and processing unit comprising:
(i) a computer processor; and
(ii) a memory storing instructions executable by the computer processor;
(iii) wherein when executed by the computer processor, said instructions transform electrical signals acquired by said data acquisition and processing unit from said electrode array into a three-dimensional image by performing s-SMOOTH based reconstruction and presenting said image to said visual display device; and
(iv) wherein said s-SMOOTH based reconstruction comprises:
(1) defining a voxel-based total generalized variation (vTGV) on triangular mesh to enhance the smoothness of the reconstructed source;
(2) incorporating l 1-2 regularization to enhance the sparsity of reconstructed source;
(3) performing voxel-based total generalized variation (vTGV) and l 1-2 regularized EEG source reconstruction according to
min
u
1
2
||
Au
-
b
||
2
2
+
vTGV
(
α
1
,
α
2
)
2
(
u
)
+
α
3
||
u
||
1
-
2
,
β
where the first term is data fidelity term, the second term is vTGV regularization, and the third term is l 1-2 regularization; and
(4) using alternating direction method of multipliers (ADMM) according to:
Algorithm 1 s-SMOOTH EEG Reconstruction
Input the electrical measurements b, the sensing matrix A, the difference
operators D and E, the parameters α 1 , α 2 , α 3 , ρ and β, as well as the
stopping criteria of the algorithm.
Initialize the current density u and the auxiliary variables p, x, y, z, {tilde over (x)}, {tilde over (y)}, {tilde over (z)}
as zero vectors.
Iterate the algorithm to update the above variables as follows
{
u
←
(
A
T
A
+
ρ
(
D
T
D
+
I
)
)
-
1
(
A
T
b
+
ρD
T
(
p
+
x
-
x
~
)
+
ρ
(
z
-
z
~
)
)
p
←
(
E
T
E
+
I
)
-
1
(
(
Du
-
x
+
x
~
)
+
E
T
(
y
-
y
~
)
)
.
x
←
prox
α
1
/
ρ
(
Du
-
p
+
x
~
)
y
←
prox
α
2
/
ρ
(
Ep
+
y
~
)
z
←
prox
α
3
/
ρ
(
u
+
z
~
+
α
3
β
ρ
q
)
x
~
←
x
~
+
Du
-
p
-
x
y
~
←
y
~
+
Ep
-
y
z
~
←
z
~
+
u
-
z
+
α
3
β
ρ
q
where prox γ (x) = sign(x) ⊙ max{|x| − γ, 0} with componentwise
multiplication ⊙, also known as shrinkage operator.
End when the stopping criteria are met.
Output the reconstructed current density u.
11. An electrode-based brain imaging system, said system comprising:
(a) an ultra-high density electrode array;
(b) a data acquisition and processing unit; and
(c) an output device;
(d) the data acquisition and processing unit comprising:
(i) a computer processor; and
(ii) a memory storing instructions executable by the computer processor;
(iii) wherein when executed by the computer processor, said instructions transform electrical signals acquired by said data acquisition and processing unit from said electrode array into a three-dimensional image by performing graph Fractional-Order Total Variation (gFOTV) based reconstruction and presenting said image to said output device:
(iv) wherein said graph Fractional-Order Total Variation (gFOTV) based reconstruction comprises:
Algorithm 2 gFOTV EEG Reconstruction
Input the electrical measurements b, the sensing matrix A, the fractional-
order derivative operator D α , the parameters λ, ρ and γ, as well as the
stopping criteria of the algorithm.
Initialize the current density u and the auxiliary variables v and {tilde over (ν)} as zero
vectors.
Iterate the algorithm to update the above variables as follows
{
v
=
shrink
(
D
α
u
+
v
~
,
λ
/
ρ
)
u
=
arg
min
u
{
1
2
Au
-
b
2
2
+
ρ
2
D
α
u
-
v
+
v
~
2
2
}
=
(
A
T
A
+
ρD
α
T
D
α
)
-
1
(
A
T
b
+
ρD
α
T
(
v
-
v
~
)
)
v
~
←
v
~
+
γ
(
D
α
u
-
v
)
End when the stopping criteria are met.
Output the reconstructed current density u.
where the parameters ρ>0, γ∈(0,(√{square root over (5)}+1)/2) and the shrinkage operator is defined componentwise shrink(u,μ) i =sign(u i )max{|u i |−μ,0}, b=the electrical measurements, A=the sensing matrix, and D α the fractional order derivative operator.
12. The system of claim 11 , wherein said graph Fractional-Order Total Variation (gFOTV) based reconstruction comprises:
defining fractional-order total variation on a triangular mesh by treating the mesh as a graph and using shortest path searching to obtain different layers of neighbors; and
performing fractional-order total variation (FOTV) regularized EEG source reconstruction and using alternating direction method of multipliers (ADMM) according to:
min
u
,
v
{
1
2
||
Au
-
b
||
2
2
+
λ
||
v
||
1
}
subject
to
D
α
u
=
v
{
v
=
shrink
(
D
α
u
+
v
~
,
λ
/
ρ
)
u
=
arg
min
u
{
1
2
||
Au
-
b
||
2
2
+
ρ
2
||
D
α
u
-
v
+
v
~
||
2
2
}
=
(
A
T
A
+
ρ
D
α
T
D
α
)
-
1
(
A
T
b
+
ρ
D
α
T
(
v
-
v
~
)
)
v
~
←
v
~
+
γ
(
D
α
u
-
v
)
where the parameters ρ>0, γ∈(0,(√{square root over (5)}+1)/2) and the shrinkage operator is defined componentwise shrink(u,μ) i =sign(u i )max{|u i |−μ,0}, b=the electrical measurements, A=the sensing matrix, and D α the fractional order derivative operator.
13. The system of claim 11 , wherein said instructions when executed by the computer processor remove artifacts from the electrical signals by performing steps comprising:
subtracting motion artifacts in the analog domain, by using skin impedance levels as an indication of the motion artifact signal; and
estimating motion artifacts with an adaptive filter by simultaneously measuring skin impedance levels and the electrical signals;
wherein motion artifacts are canceled in the analog domain.
14. The system of claim 11 , wherein the output device comprises a visual display device.
15. The system of claim 11 , wherein together the ultra-high density electrode array and data acquisition and processing unit are configured for capturing functional brain information with high temporal and spatial resolution.
16. The system of claim 11 , wherein said electrode array comprises from about 64 to about 10,000 electrodes.
17. The system of claim 11 , further comprising a wireless communications interface interconnecting the electrode array and the data acquisition and processing unit.
18. The system of claim 11 , wherein said data acquisition and processing unit has a low noise input configured for acquiring said electrical signals and routing said signals to said computer processor.
19. The system of claim 11 , wherein said ultra-high density electrode array is developed using a realistic head model constructed based on high-resolution MRI from a subject.
20. The system of claim 11 , wherein said instructions when executed by said computer processor carry out a spatially focused electrode algorithm which reduces cross-talking among electrodes and improves the spatial resolution in the forward imaging by applying an optimal weighting matrix.
21. An electrode-based brain imaging system, said system comprising:
(a) an ultra-high density electrode array;
(b) a data acquisition and processing unit;
(c) a wireless communications interface interconnecting the electrode array and the data acquisition and processing unit; and
(d) a visual display device;
(e) the data acquisition and processing unit comprising:
(i) a computer processor; and
(ii) a memory storing instructions executable by the computer processor;
(iii) wherein when executed by the computer processor, said instructions transform electrical signals acquired by said data acquisition and processing unit from said electrode array into a three-dimensional image by performing graph Fractional-Order Total Variation (gFOTV) based reconstruction and presenting said image to said visual display device; and
(iv) wherein said graph Fractional-Order Total Variation (gFOTV) based reconstruction comprises:
(1) defining fractional-order total variation on a triangular mesh by treating the mesh as a graph and using shortest path searching to obtain different layers of neighbors; and
(2) performing fractional-order total variation (FOTV) regularized EEG source reconstruction and using alternating direction method of multipliers (ADMM) according to:
min
u
,
v
{
1
2
||
Au
-
b
||
2
2
+
λ
||
v
||
1
}
subject
to
D
α
u
=
v
{
v
=
shrink
(
D
α
u
+
v
~
,
λ
/
ρ
)
u
=
arg
min
u
{
1
2
||
Au
-
b
||
2
2
+
ρ
2
||
D
α
u
-
v
+
v
~
||
2
2
}
=
(
A
T
A
+
ρ
D
α
T
D
α
)
-
1
(
A
T
b
+
ρ
D
α
T
(
v
-
v
~
)
)
v
~
←
v
~
+
γ
(
D
α
u
-
v
)
where the parameters ρ>0, γ∈(0,(√{square root over (5)}+1)/2) and the shrinkage operator is defined componentwise shrink(u,μ) i =sign(u i )max{|u i |−μ,0}, b=the electrical measurements, A=the sensing matrix, and D α the fractional order derivative operator.
22. An electrode-based brain imaging system, said system comprising:
(a) an ultra-high density electrode array;
(b) a data acquisition and processing unit; and
(c) an output device;
(d) the data acquisition and processing unit comprising:
(i) a computer processor; and
(ii) a memory storing instructions executable by the computer processor;
(iii) wherein when executed by the computer processor, said instructions transform electrical signals acquired by said data acquisition and processing unit from said electrode array into a three-dimensional image by performing s-SMOOTH based reconstruction and presenting said image to said output device; and
(iv) wherein said instructions when executed by said computer processor carry out a spatially focused electrode algorithm which reduces cross-talking among electrodes and improves the spatial resolution in the forward imaging by applying an optimal weighting matrix.
23. The system of claim 22 , wherein said instructions when executed by the computer processor remove artifacts from the electrical signals by performing steps comprising:
subtracting motion artifacts in the analog domain, by using skin impedance levels as an indication of the motion artifact signal; and
estimating motion artifacts with an adaptive filter by simultaneously measuring skin impedance levels and the electrical signals;
wherein motion artifacts are canceled in the analog domain.
24. The system of claim 22 , wherein the output device comprises a visual display device.
25. The system of claim 22 , wherein together the ultra-high density electrode array and data acquisition and processing unit are configured for capturing functional brain information with high temporal and spatial resolution.
26. The system of claim 22 , wherein the ultra-high density electrode array comprises from about 64 to about 10,000 electrodes.
27. The system of claim 22 , further comprising a wireless communications interface interconnecting the electrode array and the data acquisition and processing unit.
28. The system of claim 22 , wherein said data acquisition and processing unit has a low noise input configured for acquiring said electrical signals and routing said signals to said computer processor.
29. The system of claim 22 , wherein said ultra-high density electrode array is developed using a realistic head model constructed based on high-resolution MRI from a subject.
30. An electrode-based brain imaging system, said system comprising:
(a) an ultra-high density electrode array;
(b) a data acquisition and processing unit; and
(c) an output device;
(d) the data acquisition and processing unit comprising:
(i) a computer processor; and
(ii) a memory storing instructions executable by the computer processor;
(iii) wherein when executed by the computer processor, said instructions transform electrical signals acquired by said data acquisition and processing unit from said electrode array into a three-dimensional image by performing graph Fractional-Order Total Variation (gFOTV) based reconstruction and presenting said image to said output device; and
(iv) wherein said instructions when executed by said computer processor carry out a spatially focused electrode algorithm which reduces cross-talking among electrodes and improves the spatial resolution in the forward imaging by applying an optimal weighting matrix.
31. The system of claim 30 , wherein said graph Fractional-Order Total Variation (gFOTV) based reconstruction comprises:
defining fractional-order total variation on a triangular mesh by treating the mesh as a graph and using shortest path searching to obtain different layers of neighbors; and
performing fractional-order total variation (FOTV) regularized EEG source reconstruction and using alternating direction method of multipliers (ADMM) according to:
min
u
,
v
{
1
2
Au
-
b
2
2
+
λ
v
1
}
subject
to
D
α
u
=
v
{
v
=
shrink
(
D
α
u
+
v
~
,
λ
/
ρ
)
u
=
argmin
u
{
1
2
Au
-
b
2
2
+
ρ
2
D
α
u
-
v
+
v
~
2
2
}
=
(
A
T
A
+
ρ
D
α
T
D
α
)
-
1
(
A
T
b
+
ρ
D
α
T
(
v
-
v
~
)
)
v
~
←
v
~
+
γ
(
D
α
u
-
v
)
where the parameters ρ>0, γ∈(0,(√{square root over (5)}+1)/2) and the shrinkage operator is defined componentwise shrink(u,μ) i =sign(u i )max{|u i |−μ,0}, b=the electrical measurements, A=the sensing matrix, and D α the fractional order derivative operator.
32. The system of claim 30 , wherein said instructions when executed by the computer processor remove artifacts from the electrical signals by performing steps comprising:
subtracting motion artifacts in the analog domain, by using skin impedance levels as an indication of the motion artifact signal; and
estimating motion artifacts with an adaptive filter by simultaneously measuring skin impedance levels and the electrical signals;
wherein motion artifacts are canceled in the analog domain.
33. The system of claim 30 , wherein the output device comprises a visual display device.
34. The system of claim 30 , wherein together the ultra-high density electrode array and data acquisition and processing unit are configured for capturing functional brain information with high temporal and spatial resolution.
35. The system of claim 30 , wherein said electrode array comprises from about 64 to about 10,000 electrodes.
36. The system of claim 30 , further comprising a wireless communications interface interconnecting the electrode array and the data acquisition and processing unit.
37. The system of claim 30 , wherein said data acquisition and processing unit has a low noise input configured for acquiring said electrical signals and routing said signals to said computer processor.
38. The system of claim 30 , wherein said ultra-high density electrode array is developed using a realistic head model constructed based on high-resolution MRI from a subject.