# US 12,222,413 B2 · Randomized dimension reduction for magnetic resonance image iterative reconstruction

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- Number: US 12,222,413 B2
- Document ID: US12222413B2
- Status: Granted
- Kind: B2
- Application number: 17/744,299
- Filed: 2022-05-13
- Published: 2022-12-01
- Granted: 2025-02-11
- Earliest claimed: 2021-05-14
- Assignees: The Board of Trustees of the Leland Stanford Junior University
- Applicants: The Board of Trustees of the Leland Stanford Junior University
- Inventors: Julio A. Oscanoa Aida; Frank Ong; Mert Pilanci; Shreyas S. Vasanawala
- Web page: https://patentgrep.com/patent/US12222413B2

## CPC

- G01R 33/5611: {Parallel magnetic resonance imaging, e.g. sensitivity encoding [SENSE], simultaneous acquisition of spatial harmonics [SMASH], unaliasing by Fourier encoding of the overlaps using the temporal dimension [UNFOLD], k-t-broad-use linear acquisition speed-up technique [k-t-BLAST], k-t-SENSE (structural details of arrays of sub-coils G01R33/3415)}
- A61B 5/055: involving electronic [EMR] or nuclear [NMR] magnetic resonance, e.g. magnetic resonance imaging
- G01R 33/543: {Control of the operation of the MR system, e.g. setting of acquisition parameters prior to or during MR data acquisition, dynamic shimming, use of one or more scout images for scan plane prescription (G01R33/546 takes precedence)}
- G06T 12/20: Inverse problem, i.e. transformations from projection space into object space
- G01R: MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES (indicating correct tuning of resonant circuits H03J3/12)
- A61B: DIAGNOSIS; SURGERY; IDENTIFICATION (usefulness limited to only animals A61D)
- G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL

## Abstract

In a method for magnetic resonance imaging pseudorandomly undersampled k-space imaging data is acquired with multiple receiver coils of an MRI imaging apparatus. MR image reconstruction is performed to produce a reconstructed MR image from the k-space imaging data by iteratively solving sketched approximations of an original reconstruction problem. The sketched approximations use a sketched model matrix As that is a lower-dimensional version of an original model matrix A of the original reconstruction problem. The sketched model matrix As preserves the Fourier structure of the MR reconstruction problem and reduces the number of coils actively used during reconstruction.

## Claims

### Claim 1

A method for magnetic resonance imaging comprising:
acquiring with multiple receiver coils of an MRI imaging apparatus pseudorandomly undersampled k-space imaging data;
performing MR image reconstruction to produce a reconstructed MR image from the pseudorandomly undersampled k-space imaging data;
wherein the reconstruction comprises iteratively solving sketched approximations of an original reconstruction problem, wherein the sketched approximations use a sketched model matrix As that is a lower-dimensional version of an original model matrix A of the original reconstruction problem;
wherein the sketched model matrix As preserves the Fourier structure of the MR reconstruction problem and reduces the number of coils actively used during reconstruction.

### Claim 2 (depends on 1)

The method of claim 1 wherein the pseudorandomly undersampled k-space imaging data have both spatial and temporal dimensions.

### Claim 3 (depends on 1)

The method of claim 1 wherein iteratively solving the sketched approximations of the original reconstruction problem comprises iteratively solving second-order Taylor approximations with a sketched Hessian that includes the sketched model matrix As.

### Claim 4 (depends on 1)

The method of claim 1 wherein the sketched model matrix As is related to the original model matrix A by Ats=StA, where S is a structured sketching matrix.

### Claim 5 (depends on 4)

The method of claim 4 wherein the structured sketching matrix S is the product of two matrices SPCA and SR, where SPCA estimates virtual coils from principal components and SR sketches the virtual coils.

### Claim 6 (depends on 5)

The method of claim 5 wherein SR sketches a reduced number of high-energy virtual coils and also includes random linear combinations of remaining low-energy coils.

### Claim 7 (depends on 5)

The method of claim 5 wherein multiplication of SPCA by a coil sensitivity map operator C produces a sensitivity map operator CPCA with virtual coils sorted according to descending energy.