Methods and apparatus for joint image reconstruction and coil sensitivity estimation in parallel MRI
A method of parallel magnetic resonance imaging (pMRI) comprising acquiring pMRI signals simultaneously through a plurality of receiving coils, wherein each coil has a localized sensitivity with respect to an imaged volume; jointly estimating values for the imaged volume and for a sensitivity function for at least one of the plurality of receiving coils; and transmitting the reconstructed image to a device.
1. A method of parallel magnetic resonance imaging (pMRI) comprising:
applying one or more RF pulses in combination with one or more gradient encoding processes;
acquiring resultant pMRI signals simultaneously through a plurality of receiving coils, wherein each coil has a localized sensitivity with respect to an imaged volume;
simultaneously estimating a first set of values for a function which represents the imaged volume and a second set of values for a sensitivity function for at least one of the plurality of receiving coils, wherein the first and second sets of values are simultaneously estimated based at least in part on gradient encoding functions associated with the gradient encoding processes; and
transmitting the first set of values to a device.
2. The method of claim 1 , wherein simultaneously estimating comprises minimizing a cost function.
3. The method of claim 1 , wherein simultaneously estimating comprises finding a penalized least-squares solution and minimizing a cost function.
4. The method of claim 1 , wherein the device comprises at least one of a storage device, a printing device, and a display device.
5. The method of claim 1 , wherein acquiring resultant pMRI signals comprises acquiring pMRI signals using at least one of a Cartesian trajectory, a spiral trajectory, and a radial trajectory.
6. The method of claim 1 , wherein acquiring resultant pMRI signals comprises acquiring resultant pMRI signals in two dimensional k-space or three dimensional k-space.
7. A method of parallel magnetic resonance imaging (pMRI) comprising:
(a) acquiring pMRI signals simultaneously through a plurality of receiving coils, wherein each coil has a localized sensitivity with respect to an imaged volume;
(b) using at least some of the acquired pMRI signals to estimate a sensitivity function for at least one of the plurality of receiving coils;
(c) reconstructing an image of a sample from the pMRI signals from the plurality of receiving coils using the estimated sensitivity function;
(d) using the reconstructed image to provide new estimates of the sensitivity function for at least one of the plurality of receiving coils;
(e) iteratively repeating steps (c)-(d) at least once; and
(f) transmitting the reconstructed image to a device,
wherein the acquired pMRI signals comprise variable density data including auto-calibration signal (ACS) lines, wherein the ACS lines are used in step (b) to estimate a sensitivity function for at least one of the plurality of receiving coils.
8. The method of claim 7 , wherein transmitting the reconstructed image to a device comprises at least one of: saving the reconstructed image to storage media, printing the reconstructed image on a printing device, and displaying the reconstructed image on a display device.
9. The method of claim 7 , wherein acquiring pMRI signals comprises acquiring pMRI signals using at least one of a Cartesian trajectory, a spiral trajectory, and a radial trajectory.
10. The method of claim 7 , wherein acquiring pMRI signals comprises acquiring pMRI signals in two dimensional k-space or three dimensional k-space.
11. The method of claim 7 , wherein the acquired pMRI signals comprise variable density data.
12. The method of claim 7 , wherein substantially all of the acquired pMRI signals are used to estimate a sensitivity function for at least one of the plurality of receiving coils.
13. The method of claim 7 , wherein the pMRI signals are acquired using a Cartesian trajectory.
14. The method of claim 7 , wherein the pMRI signals are acquired using a spiral trajectory.
15. The method of claim 7 , wherein the sensitivity function for at least one of the plurality of receiving coils is a polynomial function.
16. The method of claim 7 , further comprising jointly estimating the image of the sample and the sensitivity functions for at least one of the plurality of receiving coils using a penalized least-squares solution.
17. The method of claim 16 , wherein a greedy iterative algorithm is used to jointly estimate the image of the sample and the sensitivity functions for at least one of the plurality of receiving coils.
18. The method of claim 16 , wherein jointly estimating using the penalized least-squares solution comprises minimizing a cost function.
19. The method of claim 16 , wherein jointly estimating further comprises uses a penalized least-squares solution given by
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and minimizing the cost function U given by
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where a designates the sensitivity functions for at least one of the plurality of receiving coils, f designates the image of the sample, and d is a vector comprising the acquired pMRI signals.