# US 11,079,456 B2 · Method of reconstructing magnetic resonance image data

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- Number: US 11,079,456 B2
- Document ID: US11079456B2
- Status: Granted
- Kind: B2
- Application number: 16/409,070
- Filed: 2019-05-10
- Published: 2019-11-14
- Granted: 2021-08-03
- Earliest claimed: 2018-05-10
- Assignees: Siemens Healthcare GmbH
- Applicants: Siemens Healthcare GmbH; King's College London
- Inventors: Rene Botnar; Aurelien Bustin; Radhouene Neji; Claudia Prieto
- Web page: https://patentgrep.com/patent/US11079456B2

## CPC

- G06F 17/11: for solving equations {, e.g. nonlinear equations, general mathematical optimization problems (optimization specially adapted for a specific administrative, business or logistic context G06Q10/04)}
- A61B 5/055: involving electronic [EMR] or nuclear [NMR] magnetic resonance, e.g. magnetic resonance imaging
- A61B 5/721: {using a separate sensor to detect motion or using motion information derived from signals other than the physiological signal to be measured}
- A61B 5/7292: {Prospective gating, i.e. predicting the occurrence of a physiological event for use as a synchronisation signal}
- G01R 33/4822: {in three dimensions}
- 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)}
- G01R 33/565: Correction of image distortions, e.g. due to magnetic field inhomogeneities
- G01R 33/56509: {due to motion, displacement or flow, e.g. gradient moment nulling (G01R33/567 takes precedence)}
- G01R 33/5676: {Gating or triggering based on an MR signal, e.g. involving one or more navigator echoes for motion monitoring and correction}
- G06F 18/2136: based on sparsity criteria, e.g. with an overcomplete basis
- G06T 12/20: Inverse problem, i.e. transformations from projection space into object space
- G06T 12/30: Image post-processing, e.g. metal artefact correction
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- A61B: DIAGNOSIS; SURGERY; IDENTIFICATION (usefulness limited to only animals A61D)
- G01R: MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES (indicating correct tuning of resonant circuits H03J3/12)
- G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL

## Abstract

A method of reconstructing magnetic resonance (MR) image data from k-space data. The method includes obtaining k-space data of an image region of a subject; and reconstructing, using a sparse image coding procedure, the MR image data from the k-space data by performing an iterative optimization method. The optimization method includes a data consistency iteration step and a denoising iteration step applied to MR image data generated by the data consistency iteration step. The denoising iteration step incorporates a sparsifying operation to provide a sparse representation of the MR image data for the imaged region as an input to the data consistency iteration step.

## Claims

### Claim 1

A method of reconstructing a magnetic resonance (MR) image from k-space data, the method comprising:
providing a computer with k-space data of an image of a subject; and
in said computer, performing a reconstructing algorithm, using a sparse image coding procedure in order to reconstruct, the MR image from the k-space data with iterative optimization comprising:
a data consistency iteration step comprising a determination of a difference between the reconstructed MR image transformed into k-space and the provided k-space data, wherein the determination of the difference comprises determining an l2-norm of the result of the difference between the provided k-space data and the reconstructed MR image transformed into k-space; and
a denoising iteration step applied to an MR image generated by the data consistency iteration step, wherein the denoising iteration step incorporates a sparsifying operation to provide a sparse representation of the MR image for the imaged region as an input to the data consistency iteration,
wherein the denoising iteration step is of the form
x
^
=
arg
⁢
⁢
min
x
⁢
h
⁡
(
x
)
,
h
⁡
(
x
)
,
h(x) is a function defined as {sparse consistency component in image space+λ(sparse coefficients associated with a synthesis dictionary for the sparse representation of the MR image data)}, and λ is a sparsity-control parameter a value of which is adjustable to adjust a strength of sparsity for the sparse representation of the MR image.

### Claim 2 (depends on 1)

A method as claimed in claim 1, wherein the data consistency iteration step comprises minimising an Augmented Lagrangian with respect to the reconstructed MR image.

### Claim 3 (depends on 1)

A method as claimed in claim 1, wherein the denoising iteration step comprises minimising an Augmented Lagrangian with respect to sparse coefficients associated with a synthesis dictionary for the sparse representation of the MR image.

### Claim 4 (depends on 1)

A method as claimed in claim 1, wherein the denoising iteration step comprises a determination of the difference between the reconstructed MR image and the sparse representation of the MR image.

### Claim 5 (depends on 4)

A method as claimed in claim 4, wherein the determination of the difference comprises determining a l2-norm of a result of a subtraction of the sparse representation of the MR image from the reconstructed MR image.

### Claim 6 (depends on 1)

A method as claimed in claim 1, wherein the data consistency iteration step of an optimization problem is of the form
x
^
=
arg
⁢
⁢
min
x
⁢
f
⁡
(
x
)
,
wherein ƒ(x) is a function defined as {data consistency component in k-space+μ(sparse consistency component in image space)}, wherein μ is a regularization parameter.

### Claim 7 (depends on 1)

A method as claimed in claim 1, wherein the sparsifying operation of the denoising iteration step is applied to sparse coefficients associated with a synthesis dictionary for the sparse representation of the MR image, whereby sparse coefficients having a value below a threshold value are set to zero.

### Claim 8 (depends on 7)

A method as claimed in claim 7, wherein the threshold value is equal to the value of the sparsity-control parameter.

### Claim 9 (depends on 1)

A non-transitory computer readable medium comprising instructions recorded thereon which, when executed by a computer, cause the computer to perform the method as claimed in claim 1.

### Claim 10

A magnetic resonance (MR) apparatus, comprising:
a gradient system configured to apply a magnetic field gradient;
an excitation system configured to apply an excitation pulse to a subject and to receive signals from the subject; and
a computing system configured:
to receive the signals from the excitation system,
to execute program code to control the gradient system and the excitation system to acquire k-space data of an image of a subject, and a plurality of navigator signals for the image of the subject,
to reconstruct, using a sparse image coding procedure, an MR image from the acquired k-space data by performing an iterative optimization method comprising:
a data consistency iteration step comprising a determination of a difference between the reconstructed MR image transformed into k-space and the provided k-space data, wherein the determination of the difference comprises determining an l2-norm of the result of the difference between the provided k-space data and the reconstructed MR image transformed into k-space; and
a denoising iteration step applied to MR image generated by the data consistency iteration step, wherein the denoising iteration step incorporates a sparsifying operation to provide a sparse representation of the MR image for the image of the subject as an input to the data consistency iteration step.