Sparse approximate encoding of Wave-CAIPI: preconditioner and noise reduction
Described here are systems and methods for producing images of a subject using magnetic resonance imaging (“MRI”) in which data are acquired using a sparse approximate encoding scheme for controlled aliasing techniques. As one example, the sparse approximate encoding can be used for a Wave-CAIPI encoding scheme, which can enable faster image reconstruction using fewer computational resources, in addition to reducing noise in the reconstructed images relative to those reconstructed from data acquired using a Wave-CAIPI encoding scheme without sparse approximate encoding.
1. A method for reconstructing an image of a subject using a magnetic resonance imaging (MRI) system, the steps of the method comprising:
(a) accessing with a computer system, data acquired from a subject using an MRI system and an RF coil array, wherein the data were acquired using an encoding scheme that distributes aliased spatial frequency information in three dimensions in k-space; and
(b) reconstructing an image of the subject from the data using the computer system by inputting the data to an iterative reconstruction algorithm that solves an image reconstruction problem by implementing a sparse approximate encoding matrix as a preconditioner on the reconstruction problem, generating output as the reconstructed image, wherein the preconditioner removes a dependency of the reconstruction problem on a channel count of the RF coil array and over-sampling factors.
2. The method as recited in claim 1 , wherein the sparse approximate encoding matrix is a sparse block Toeplitz matrix.
3. The method as recited in claim 1 , wherein the sparse approximate encoding matrix is scaled with sensitivity weights.
4. The method as recited in claim 3 , wherein the sensitivity weights are contained in coil sensitivity data accessed with the computer system.
5. The method as recited in claim 1 , wherein a size of blocks in the sparse approximate encoding matrix is selected as a number of readout voxels.
6. The method as recited in claim 1 , wherein a number of blocks in the sparse approximate encoding matrix is selected based on an acceleration factor used when acquiring the data.
7. The method as recited in claim 1 , wherein step (b) includes binning the data based on similarities of data in each bin, wherein the similarities are related to an incoherency of the encoding scheme.
8. The method as recited in claim 7 , wherein the similarities of the data in each bin are modeled using a low-rank representation.
9. The method as recited in claim 1 , wherein the sparse approximate encoding matrix assumes that a given readout position is coupled only to voxels that are separated away from the given readout position by an integer multiple of a number of cycles played out when acquiring the data.
10. The method as recited in claim 9 , wherein the sparse approximate encoding matrix has a sparse block Toeplitz structure.
11. The method as recited in claim 10 , wherein the sparse block Toeplitz structure is comprised of blocks having a size determined by a number of readout voxels.
12. The method as recited in claim 10 , wherein the sparse block Toeplitz structure is comprised of blocks, wherein a number of the blocks is determined based on an acceleration factor used when acquiring the data.
13. The method as recited in claim 1 , wherein the preconditioner removes the dependency of the reconstruction problem on the array coil channel count and over-sampling factors by approximating an encoding matrix used in the reconstruction problem by assuming an encoding sparsity pattern that is based on a number of cycles played out in an imaging pulse sequence used when acquiring the data with the MRI system.
14. The method as recited in claim 1 , wherein the preconditioner removes the dependency of the reconstruction problem on the array coil channel count and over-sampling factors by approximating an encoding matrix by assuming that each voxel along the readout direction in the reconstructed image is only coupled to other voxels that are separated by an integer multiple of the number of cycles away from that voxel.