Variable density incoherent spatiotemporal acquisition (VISTA) for highly accelerated magnetic resonance imaging
A pseudo-random, incoherent sampling technique, called Variable density Incoherent Spatiotemporal Acquisition (VISTA) is disclosed, which is based on minimal Riesz energy problem. Compared with other pseudorandom methods (e.g., PDS), VISTA has the unique ability to incorporate a variety of problem-specific constraints. In this study, VISTA was applied to real-time CMR, where it not only provided an incoherent sampling with variable density but also ensured a constant temporal resolution and a fully sampled time-averaged data.
1. A method of Variable density Incoherent Spatiotemporal Acquisition (VISTA) for generating magnetic resonance imaging (MRI) sampling location of N data samples on an n-dimensional (nD) grid, comprising;
initializing a location of N k-space samples on the nD grid;
iteratively minimizing a cost function U to update the location of samples;
enforcing application specific constraints on the distribution of samples in each iteration;
generating a sampling pattern at each iteration; and
storing each sampling pattern as a lookup table, whereby MR images are reconstructed from the data collected using the lookup table.
2. The method of claim 1 , if the convergence has not occurred, repeating the minimizing and enforcing.
3. The method of claim 1 , wherein a deterministic, random, or pseudorandom sampling is used as the initializing.
4. The method of claim 1 , where the number of samples, N, is predefined by the user.
5. The method of claim 1 , wherein gradient projections are applied to enforce application-specific constraints.
6. The method of claim 1 , wherein a constraint is enforced such that averaging the samples along one of the n dimensions yields fully sampled data in (n−1)-dimensional domain.
7. The method of claim 1 , wherein the location of samples is rounded to the nearest location on a Cartesian grid.
8. The method of claim 1 , wherein partial-Fourier sampling is embedded into the VISTA framework by imposing antipodal symmetry on the sampling pattern.
9. The method of claim 1 , further comprising different sampling domains, including: 3D spatial MRI (with 2D VISTA in k y -k z domain); 2D cine at rest and stress (with 2D VISTA in k y -t domain); 3D cine at rest and stress (with 3D VISTA in k y -k z -t domain); 2D and 3D multi-direction flow imaging (with 3D VISTA in k y -t-velocity encoding domain and 4D VISTA in k y -k z t-velocity encoding domain, respectively); 2D myocardial perfusion (with 2D VISTA in k y -t domain); 3D myocardial perfusion (with 3D VISTA in k y -k z -t domain); 3D dynamic angiography (with 3D VISTA in k y -k z -t domain); and 2D and 3D MR elastography (with 2D VISTA in k y -phase offset domain and 3D VISTA in k y -k z -phase offset domain, respectively).
10. The method of claim 1 , for 2D and 3D single-point acquisition for electron paramagnetic resonance imaging.
11. The method of claim 1 , further comprising sampling in Cartesian and non-Cartesian domains, where one or more dimensions represent a variable other than space or time.
12. The method of claim 1 , wherein the resulting sampling pattern is used for iterative or non-iterative image reconstruction methods.
13. The method of claim 1 , wherein the distribution is obtained before full convergence is reached.
14. The method in claim 1 , wherein a sample represents multiple k-space lines obtained by EPI sequence or an arm of a spiral or radial acquisition.
15. The method if claim 1 , wherein one or more transmit and receive coils are used for acquisition.
16. The method of claim 1 , wherein the cost function is represented by:
U
(
c
,
s
,
ω
N
)
=
1
2
∑
i
=
1
N
∑
j
≠
i
c
(
v
→
i
)
c
(
v
→
j
)
v
→
i
-
v
→
j
W
s
,
with
s
>
0
and
ω
N
⋐
𝒞
(
4
)
wherein, the column vector {right arrow over (ν)} i defines the Cartesian coordinates of the i th sample on the grid, constraints are defined via , and ∥{right arrow over (ν)} i ∥ W s =({right arrow over (ν)} i T W{right arrow over (ν)} i ) s/2 ,with diagonal matrix W specifying the relative scaling of different dimensions.
17. The method of claim 16 , wherein periodic or non-periodic boundary conditions are enforced.
18. The method of claim 16 , wherein c({right arrow over (ν)}) is defined by parametric or nonparametric functions.
19. The method of claim 16 , wherein the cost function U is iteratively minimized using a gradient based optimization methods.
20. The method of the claim 16 , wherein a negative of the steepest descent for an i th sample is given by a relationship:
∇
→
U
i
=
-
∑
j
≠
i
(
sc
(
v
→
i
)
c
(
v
→
j
)
W
[
v
→
i
-
v
→
j
]
v
→
i
-
v
→
j
W
s
+
2
-
c
(
v
→
j
)
∇
→
c
(
v
→
i
)
v
→
i
-
v
→
j
W
s
)
,
wherein {right arrow over (∇)}c({right arrow over (ν)} i ) is the gradient of c({right arrow over (ν)}) at {right arrow over (ν)} i , and W[{right arrow over (ν)} i −{right arrow over (ν)} j ] represents a matrix-vector multiplication.
21. A computer implemented apparatus for performing generating magnetic resonance imaging (MRI) using variable density incoherent Spatiotemporal Acquisition (VISTA), comprising;
a memory;
a processor; and
computer executable instructions stored in the memory that when executed on the processor perform a method comprising:
initializing a location of N k-space samples on the nD grid;
iteratively minimizing a cost function U to update the location samples;
enforcing application specific constraints on the distribution of samples in each iteration;
generating a sampling pattern at each iteration; and
storing each sampling pattern as a lookup table, whereby MR images are reconstructed from the data collected using the lookup table.
22. The apparatus of claim 21 , wherein if the convergence has not occurred, the minimizing and enforcing constraints is repeated.