Generalized MRI reconstruction with correction for multiple image distortion
View Patent ↗Disclosed is an effective algorithm to correct motion-induced phase error using an iterative reconstruction. Using a conjugate-gradient (CG) algorithm, the phase error is treated as an image encoding function. Given the complex perturbation terms, diffusion-weighted images can be reconstructed using an augmented sensitivity map. The mathematical formulation and image reconstruction procedures are similar to the SENSE reconstruction. By defining a dynamic composition sensitivity, the CG phase correction method can be conveniently incorporated with SENSE reconstruction for the application of multi-shot SENSE DWI. Effective phase correction and multi-shot SENSE DWI (R=1 to 3) are demonstrated on both simulated and in vivo data acquired with PROPELLER and SNAILS.
1. A method of magnetic resonance imaging reconstruction with phase error correction comprising the steps of:
a) Obtaining data for a plurality of k-space trajectories using a plurality of receiver coils, each with a specific coil phase,
b) Defining data in terms of coil sensitivity and position vectors,
c) Modifying the coil sensitivities for each coil in step (b) to include a time invariant and time variant phase perturbation caused by (i) motion during diffusion encoding, and (ii) at off resonance blurring, and
d) Iteratively reconstructing the data to form image data for image reconstruction by employing an iterative conjugate gradient reconstruction.
2. The method, as defined by claim 1 , wherein the iterative conjugate gradient reconstruction, comprises the steps of:
reformulating a reconstruction problem into: (E H E)v=E H m , where
v is a voxel matrix, E is an image encoding matrix comprising the modified coil sensitivities and a discrete Fourier Transform, and m is a vector containing the acquired k-space sampling data;
precomputing E H m once;
initialize v (0) ; and
solving for v iteratively by computing (E H E)v (n) , where n indicates an iteration step, so that v converges to a solution that minimizes a norm∥(E H E)v (n) −E H m∥.
3. The method as defined by claim 1 wherein step (d) utilizes a Hermetian matrix.
4. The method as defined by claim 1 wherein step (a) employs variable-density spiral acquisitions from which navigator phase and coil sensitivity are acquired.
5. The method as defined by claim 1 wherein data obtained in step (a) is expressed as
m
(
k
l
)
=
∑
ρ
=
1
N
*
N
s
γ
(
r
ρ
)
v
(
r
ρ
)
ⅇ
-
j
k
l
r
ρ
where
s γ =coil sensitivity
r (ρ) =position vector
V=voxel
e −jk i r ρ =image coding.
6. The method as defined by claim 5 wherein step (c) includes in the step (a) expression of data a term p(r ρ ) for time invariant phase, but variable between RF excitation/diffusion-encoding, whereby the expression for data, for each interleave, becomes
m
(
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ρ
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1
N
*
N
s
γ
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r
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p
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r
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v
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r
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ⅇ
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k
l
r
ρ
7. The method as defined by claim 6 wherein step (d) includes in the step (a) expression of data a term o(r ρ (iΔt)) for time variant phase whereby the expression for data becomes
m
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k
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i
Δ
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γ
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o
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r
ρ
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i
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v
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ⅇ
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k
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8. The method of claim 7 wherein the time invariant phase and the time variant phase become part of an augmented sensitivity and the expression for data becomes
s
~
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p
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o
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.
9. The method as defined by claim 8 wherein step (a) employs diffusion-weighted imaging with multi-shot image acquisition.
10. The method as defined by claim 1 wherein step (a) employs diffusion-weighted imaging with multi-shot image acquisition.
11. The method as defined in claim 1 , wherein the time variant phase perturbation is also spatially variable and wherein the motion during diffusion encoding varies between interleaves, blades, and k-space lines following each RF excitation and diffusion encoding step, and wherein the off resonance blurring continuously accrues a phase angle during each interleaf and blade and k-space line, and wherein the conjugate gradient reconstruction is linear and non-linear.
12. The method, as defined by claim 1 , wherein the iterative conjugate gradient reconstruction, comprises the steps of:
reformulating a reconstruction problem into: (E H E)v=E H m, where
v is a voxel matix, E is an image encoding matrix comprising the modified coil sensitivities and a discrete Fourier Transform, and m is a vector containing the acquired k-space sampling data;
precomputing E H m once;
initialize v (0) ; and
solving for v iteratively by computing (E H E)v (n) , where n indicates an iteration step, so that v converges to a solution that minimizes a norm ∥(E H E)v (n) −E H m∥.
13. The method as defined by claim 12 , wherein data obtained in step (a) is expressed as
m
(
k
l
(
i
Δ
t
)
)
=
∑
ρ
=
1
N
*
N
s
γ
(
r
ρ
)
o
(
r
ρ
(
i
Δ
t
)
)
v
(
r
ρ
)
ⅇ
-
jk
l
r
ρ
where
s γ =coil sensitivity
o(r ρ (iΔt))=off-resonance phase
r (ρ) =position vector
v=voxel.
14. The method as defined by claim 13 wherein step (c) includes in the step (a) expression of data a term p(r ρ ) for time invariant phase, but variable between RF excitation/diffusion-encoding, whereby the expression for data, for each interleave, becomes
m
(
k
l
)
=
∑
ρ
=
1
N
*
N
s
γ
(
r
ρ
)
p
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v
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r
ρ
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ⅇ
-
j
k
l
r
ρ
15. The method as defined by claim 14 wherein step (d) includes in the step (a) expression of data a term o(r ρ (iΔt)) for time variant phase whereby the expression for data becomes
m
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γ
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v
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k
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r
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16. The method of claim 15 wherein the time invariant phase and the time variant phase become part of an augmented sensitivity and the expression for data becomes
s
~
γ
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r
ρ
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Δ
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=
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γ
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p
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o
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.
17. The method as defined by claim 16 wherein step (a) employs diffusion-weighted imaging with multi-shot image acquisition.
18. A method of magnetic resonance imaging reconstruction with phase error correction comprising the steps of:
a. Obtaining data for a plurality of k-space trajectories using a plurality of receiver coils, each with a specific coil magnitude and phase,
b. Defining data in terms of coil sensitivity and position vectors,
c. Modifying the coil sensitivities for each coil in step (b) to include a time variant spatially variable phase perturbation caused by (i) motion during diffusion encoding, which varies between interleaves, blades, and k-space lines following each RF excitation or diffusion step, and (ii) spins at off-resonance, which continuously accrue a phase angle during each interface, blade, and k-line, and
d. Iteratively reconstructing the data to form image data for image reconstruction by employing an iterative conjugate gradient reconstruction or similar algorithms for large matrix systems.