### Abstract

To reconstruct magnetic resonance (MR) images from undersampled Cartesian k-space data, we propose an algorithm based on two deep-learning architectures: (1) a multi-layer perceptron (MLP) that estimates a target image from 1D inverse Fourier transform (IFT) of k-space; and (2) a convolutional neural network (CNN) that estimates the target image from the estimated image of the MLP. The MLP learns the relationship between 1D IFT of undersampled k-space which is transformed along the frequency-encoding direction and the target fully-sampled image. The MLP is trained line by line rather than by a whole image, because each frequency-encoding line of the 1D IFT of k-space is not correlated with each other. It can dramatically decrease the number of parameters to be learned because the number of input/output pixels decrease from N^{2} to N. The next CNN learns the relationship between an estimated image of the MLP and the target fully-sampled image to reduce remaining artifacts in the image domain. The proposed deep-learning algorithm (i.e., the combination of the MLP and the CNN) exhibited superior performance over a single MLP and a single CNN. And it outperformed the comparison algorithms including CS-MRI, DL-MRI, a CNN-based algorithm (denoted as Wang’s algorithm), PANO, and FDLCP in both qualitative and quantitative evaluation. Consequently, the proposed algorithm is applicable up to a sampling ratio of 25% in Cartesian k-space.

Original language | English |
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Title of host publication | Medical Image Computing and Computer Assisted Intervention – MICCAI 2018 - 21st International Conference, 2018, Proceedings |

Editors | Julia A. Schnabel, Christos Davatzikos, Carlos Alberola-López, Gabor Fichtinger, Alejandro F. Frangi |

Publisher | Springer Verlag |

Pages | 241-249 |

Number of pages | 9 |

ISBN (Print) | 9783030009274 |

DOIs | |

Publication status | Published - 2018 Jan 1 |

Event | 21st International Conference on Medical Image Computing and Computer Assisted Intervention, MICCAI 2018 - Granada, Spain Duration: 2018 Sep 16 → 2018 Sep 20 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11070 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 21st International Conference on Medical Image Computing and Computer Assisted Intervention, MICCAI 2018 |
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Country | Spain |

City | Granada |

Period | 18/9/16 → 18/9/20 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Medical Image Computing and Computer Assisted Intervention – MICCAI 2018 - 21st International Conference, 2018, Proceedings*(pp. 241-249). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11070 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-00928-1_28

}

*Medical Image Computing and Computer Assisted Intervention – MICCAI 2018 - 21st International Conference, 2018, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11070 LNCS, Springer Verlag, pp. 241-249, 21st International Conference on Medical Image Computing and Computer Assisted Intervention, MICCAI 2018, Granada, Spain, 18/9/16. https://doi.org/10.1007/978-3-030-00928-1_28

**Translation of 1D inverse fourier transform of k-space to an image based on deep learning for accelerating magnetic resonance imaging.** / Eo, Taejoon; Shin, Hyungseob; Kim, Taeseong; Jun, Yohan; Hwang, Do Sik.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Translation of 1D inverse fourier transform of k-space to an image based on deep learning for accelerating magnetic resonance imaging

AU - Eo, Taejoon

AU - Shin, Hyungseob

AU - Kim, Taeseong

AU - Jun, Yohan

AU - Hwang, Do Sik

PY - 2018/1/1

Y1 - 2018/1/1

N2 - To reconstruct magnetic resonance (MR) images from undersampled Cartesian k-space data, we propose an algorithm based on two deep-learning architectures: (1) a multi-layer perceptron (MLP) that estimates a target image from 1D inverse Fourier transform (IFT) of k-space; and (2) a convolutional neural network (CNN) that estimates the target image from the estimated image of the MLP. The MLP learns the relationship between 1D IFT of undersampled k-space which is transformed along the frequency-encoding direction and the target fully-sampled image. The MLP is trained line by line rather than by a whole image, because each frequency-encoding line of the 1D IFT of k-space is not correlated with each other. It can dramatically decrease the number of parameters to be learned because the number of input/output pixels decrease from N2 to N. The next CNN learns the relationship between an estimated image of the MLP and the target fully-sampled image to reduce remaining artifacts in the image domain. The proposed deep-learning algorithm (i.e., the combination of the MLP and the CNN) exhibited superior performance over a single MLP and a single CNN. And it outperformed the comparison algorithms including CS-MRI, DL-MRI, a CNN-based algorithm (denoted as Wang’s algorithm), PANO, and FDLCP in both qualitative and quantitative evaluation. Consequently, the proposed algorithm is applicable up to a sampling ratio of 25% in Cartesian k-space.

AB - To reconstruct magnetic resonance (MR) images from undersampled Cartesian k-space data, we propose an algorithm based on two deep-learning architectures: (1) a multi-layer perceptron (MLP) that estimates a target image from 1D inverse Fourier transform (IFT) of k-space; and (2) a convolutional neural network (CNN) that estimates the target image from the estimated image of the MLP. The MLP learns the relationship between 1D IFT of undersampled k-space which is transformed along the frequency-encoding direction and the target fully-sampled image. The MLP is trained line by line rather than by a whole image, because each frequency-encoding line of the 1D IFT of k-space is not correlated with each other. It can dramatically decrease the number of parameters to be learned because the number of input/output pixels decrease from N2 to N. The next CNN learns the relationship between an estimated image of the MLP and the target fully-sampled image to reduce remaining artifacts in the image domain. The proposed deep-learning algorithm (i.e., the combination of the MLP and the CNN) exhibited superior performance over a single MLP and a single CNN. And it outperformed the comparison algorithms including CS-MRI, DL-MRI, a CNN-based algorithm (denoted as Wang’s algorithm), PANO, and FDLCP in both qualitative and quantitative evaluation. Consequently, the proposed algorithm is applicable up to a sampling ratio of 25% in Cartesian k-space.

UR - http://www.scopus.com/inward/record.url?scp=85054073010&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85054073010&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-00928-1_28

DO - 10.1007/978-3-030-00928-1_28

M3 - Conference contribution

AN - SCOPUS:85054073010

SN - 9783030009274

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 241

EP - 249

BT - Medical Image Computing and Computer Assisted Intervention – MICCAI 2018 - 21st International Conference, 2018, Proceedings

A2 - Schnabel, Julia A.

A2 - Davatzikos, Christos

A2 - Alberola-López, Carlos

A2 - Fichtinger, Gabor

A2 - Frangi, Alejandro F.

PB - Springer Verlag

ER -