# US 2013/0279781 A1 · Method for estimating a grappa reconstruction kernel

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- Number: US 2013/0279781 A1
- Document ID: US20130279781A1
- Status: Published application
- Kind: A1
- Application number: 13/804,147
- Filed: 2013-03-14
- Published: 2013-10-24
- Earliest claimed: 2012-04-19
- Assignees: The Ohio State University
- Applicants: The Ohio State University
- Inventors: Yu Ding; Orlando Simonetti
- Web page: https://patentgrep.com/patent/US20130279781A1

## CPC

- G01R 33/5608: {Data processing and visualization specially adapted for MR, e.g. for feature analysis and pattern recognition on the basis of measured MR data, segmentation of measured MR data, edge contour detection on the basis of measured MR data, for enhancing measured MR data in terms of signal-to-noise ratio by means of noise filtering or apodization, for enhancing measured MR data in terms of resolution by means for deblurring, windowing, zero filling, or generation of gray-scaled images, colour-coded images or images displaying vectors instead of pixels (image data processing or generation, in general G06T)}
- G01R 33/4818: {MR characterised by data acquisition along a specific k-space trajectory or by the temporal order of k-space coverage, e.g. centric or segmented coverage of k-space}
- 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)}
- G06T 15/00: Three-dimensional [3D] image rendering
- G01R 33/56308: {Characterization of motion or flow; Dynamic imaging}
- 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 for improving the signal-to-noise ratio (SNR) of TGRAPPA. The SNR of the ACS lines is proportional to the condition number of the GRAPPA kernel encoding equations. Therefore, the GRAPPA kernel estimated from higher SNR ACS lines amplifies the random noise in GRAPPA reconstruction. In TGRAPPA reconstruction of dynamic image series, a widely used method to acquire ACS lines is to average-all-frame (AAF). The present disclosure utilizes a tile-all-frame (TAF) as ACS lines to improve the SNR of the reconstructed images.

## Claims

### Claim 1

A method of determining a k-space convolution kernel in GRAPPA reconstruction of magnetic resonance imaging, comprising:
acquiring plural frames of 2-D images or 3-D images at a same slice location (2-D) or slab location (3-D);
acquiring k-space data of the plural frames of 2-D images or 3-D images;
providing at least two sets of ACS lines from the acquired k-space data; and
utilizing a number of linear equations estimate the k-space convolution kernel that is greater than a number of linear equations that could be derived from one set of ACS lines.

### Claim 2 (depends on 1)

The method of claim 1, further comprising applying a linear regression to at least two sets of ACS lines to estimate the k-space convolution kernel.

### Claim 3 (depends on 2)

The method of claim 2, wherein a well-posedness of the linear equations used to estimate the k-space convolution kernel are determined in accordance with a condition number.

### Claim 4 (depends on 3)

The method of claim 3, wherein the condition number is affected by the signal-to-noise ratio in the ACS lines.

### Claim 5 (depends on 3)

The method of claim 3, further comprising combining the linear equations with any type of regularization to estimate the k-space convolution kernel.

### Claim 6 (depends on 2)

The method of claim 2, wherein the linear regression is defined by the relationship:
AG=b,
wherein an m×n matrix A is the input of the GRAPPA reconstruction or other k-space based reconstructions, wherein each row of the matrix A represents a sliding window in k-space, m is the number of reconstructed k-space points/sliding window, wherein G is a vectorized GRAPPA kernel with size n×1, and wherein b is a vectorized output of the GRAPPA reconstruction with size m×1.

### Claim 7 (depends on 1)

The method of claim 1, further comprising determining multiple k-space convolution kernels.

### Claim 8

A method of determining a k-space convolution kernel in a k-space based reconstruction method that has at least one implicit k-space convolution kernel estimation step, comprising:
acquiring k-space data of plural frames of images at a same location;
providing at least two sets of ACS lines from the acquired k-space data; and
utilizing a number of linear equations estimate the k-space convolution kernel that is greater than a number of linear equations that could be derived from one set of ACS lines.

### Claim 9 (depends on 8)

The method of claim 8, wherein a well-posedness of the linear equations used to estimate the k-space convolution kernel are determined in accordance with a condition number.

### Claim 10 (depends on 9)

The method of claim 9, wherein the condition number is affected by the signal-to-noise ratio in the ACS lines.

### Claim 11 (depends on 9)

The method of claim 9, further comprising combining the linear equations with any type of regularization to estimate the k-space convolution kernel.

### Claim 12 (depends on 8)

The method of claim 8, wherein the linear regression is defined by the relationship:
AG=b,
wherein an m×n matrix A is the input of the GRAPPA reconstruction, wherein each row of the matrix A represents a GRAPPA sliding window in k-space, m is the number of reconstructed k-space points/sliding window, wherein G is a vectorized GRAPPA kernel with size n×1, and wherein b is a vectorized output of the GRAPPA reconstruction with size m×1.

### Claim 13 (depends on 12)

The method of claim 12, wherein a number of equations m is larger than a number of equations constructed from the one set of ACS lines.

### Claim 14

A computer readable medium containing computer-executable instruction that when executed by a processor of a computing device performs a method of determining a k-space convolution kernel in GRAPPA reconstruction of magnetic resonance imaging, comprising:
acquiring plural frames of 2-D images or 3-D images at a same slice location (2-D) or slab location (3-D);
acquiring k-space data of the plural frames of 2-D images or 3-D images;
providing at least two sets of ACS lines from the acquired k-space data; and
utilizing a number of linear equations estimate the k-space convolution kernel that is greater than a number of linear equations that could be derived from one set of ACS lines.

### Claim 15 (depends on 14)

The computer readable medium of claim 14, further comprising instructions for applying a linear regression to the at least two sets of ACS lines to estimate the k-space convolution kernel.

### Claim 16 (depends on 15)

The computer readable medium of claim 15, wherein the linear equations used to estimate the k-space convolution kernel are determined in accordance with a condition number.

### Claim 17 (depends on 16)

The computer readable medium of claim 16, wherein the condition number is affected by a signal-to-noise ratio in the ACS lines.

### Claim 18 (depends on 16)

The computer readable medium of claim 16, further comprising instructions for combining the linear equations with any type of regularization to estimate the k-space convolution kernel.

### Claim 19 (depends on 15)

The computer readable medium of claim 15, wherein the linear regression is defined by the relationship:
AG=b,
wherein an m×n matrix A is the input of the GRAPPA reconstruction, wherein each row of the matrix A represents a GRAPPA sliding window in k-space, m is the number of reconstructed k-space points/sliding window, wherein G is a vectorized GRAPPA kernel with size n×1, and wherein b is a vectorized output of the GRAPPA reconstruction with size m×1.

### Claim 20 (depends on 18)

The computer readable medium of claim 18, wherein a number of equations m is larger than a number of equations constructed from the one set of ACS lines.