# PIC-GAN: A Parallel Imaging Coupled Generative Adversarial Network for Accelerated Multi-Channel MRI Reconstruction

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Problem Formulation

#### 2.2. The Proposed PIC-GAN Reconstruction Framework

#### 2.2.1. Datasets

#### 2.2.2. Comparison Studies, Experimental Settings and Evaluation

## 3. Results

#### 3.1. Reconstruction Results: Abdominal MRI Data

#### 3.2. Reconstruction Results: Knee MRI Data

#### 3.3. Quantitative Evaluations

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schema of the proposed parallel imaging and generative adversarial network (PIC-GAN) reconstruction network.

**Figure 2.**The generator $\mathrm{G}$ consists of four encoder blocks followed by corresponding 4 decoder blocks. In addition, shortcut connections are applied to connect mirrored layers between the encoder and decoder paths.

**Figure 3.**Representative abdominal images reconstructed with acceleration AF = 6. The first and second rows depict reconstruction results for regular Cartesian sampling, the third and fourth row depict the same for variable density random sampling. The PIC-GAN reconstruction shows reduced artifacts compared to other methods. (GT: Ground truth. ZF: Zero-filled. L1-ESPIRiT: Sparsity-based parallel imaging. VN: Variational network. ZF-GAN: Conventional GAN with single-channel images as input PIC-GAN: Our proposed method. Red box: Zoomed-in area.)

**Figure 4.**Visualization of the intermediate results of our PIC-GAN reconstruction. (

**a**) Undersampled image with an acceleration factor of 6× with the regular (1st row) and the random (3rd row) Cartesian sampling (

**b**–

**d**) Results from intermediate steps 500 to 2000 in the reconstruction process. (

**e**) Ground truth.

**Figure 5.**Comparison of different reconstruction methods with different acceleration factors for the knee dataset. From left to right, each column represents selected knee image reconstructed using ZF, L1-ESPIRiT, VN, ZF-GA and PIC-GAN, respectively, compared to the GT. (GT: Ground truth. ZF: Zero-filled. L1-ESPIRiT: Sparsity-based parallel imaging. VN: Variational network. ZF-GAN: Conventional GAN with single-channel images as input PIC-GAN: Our proposed method. The ZF-GAN reconstructed images were over-smoothed with blocky artifacts (yellow arrows) and obvious residual artifacts (green arrows).)

**Figure 6.**Representative knee images reconstructed with an acceleration factor of 6. The first and second rows show reconstruction results using regular Cartesian sampling, the third and fourth rows show reconstruction results using variable density random sampling. Zoomed in views (as red boxes) show that the proposed method has resulted in both sharper and cleaner reconstruction compared to the results obtained by L1-ESPIRiT, VN and ZF-GAN. Both ZF-GAN and PIC-GAN reconstruction can significantly suppress the artifacts compared to ZF and L1-ESPIRiT. (GT: Ground truth. ZF: Zero-filled. L1-ESPIRiT: Sparsity-based parallel imaging. VN: Variational network. ZF-GAN: Conventional GAN with single-channel images as input PIC-GAN: Our proposed method. ZF-GAN images contained blurred vessels (green arrows) and blocky patterns (yellow arrows).)

**Figure 7.**Performance comparisons (PSNR, SSIM and NMSE $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-5}$) on abdominal MRI data with different acceleration factors. (GT: Ground truth. ZF: Zero-filled. L1-ESPIRiT: Sparsity-based parallel imaging. VN: Variational network. ZF-GAN: Conventional GAN with single-channel images as input PIC-GAN: Our proposed method.)

**Table 1.**Performance comparisons (Normalized Mean Square Error (NMSE) $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-5}$, Structural Similarity Index (SSIM), Peak Signal to Noise Ratio (PSNR) and Average Reconstruction Time(s)) on abdominal magnetic resonance imaging (MRI) data with different acceleration factors. The bold numbers highlight the best results. The PIC-GAN outperformed the competing algorithms with significantly higher PSNR, SSIM and lower NMSE values (p < 0.05).

R | METHOD | REGULAR | RANDOM | TIME (s) | ||||
---|---|---|---|---|---|---|---|---|

PSNR | SSIM | NMSE | PSNR | SSIM | NMSE | |||

2-FOLD | ZF | 28.03 ± 2.68 | 0.90 ± 0.01 | 1.74 ± 0.94 | 34.66 ± 2.98 | 0.95 ± 0.01 | 0.49 ± 0.33 | 0.05 ± 0.01 |

L1-ESPIRiT | 33.25 ± 2.34 | 0.8 ± 0.06 | 0.62 ± 0.25 | 33.69 ± 1.48 | 0.81 ± 0.03 | 0.50 ± 0.02 | 143.71 ± 1.20 | |

VN | 34.99 ± 2.09 | 0.89 ± 0.03 | 0.51 ± 0.27 | 33.20 ± 2.82 | 0.90 ± 0.02 | 0.92 ± 0.63 | 0.38 ± 0.01 | |

ZF-GAN | 34.91 ± 2.92 | 0.93 ± 0.05 | 0.60 ± 0.33 | 37.22 ± 1.77 | 0.96 ± 0.01 | 0.32 ± 0.09 | 0.37 ± 0.00 | |

PIC-GAN | 36.60 ± 3.57 | 0.94 ± 0.02 | 0.49 ± 0.44 | 39.59 ± 2.64 | 0.97 ± 0.01 | 0.19 ± 0.13 | 0.69 ± 0.00 | |

4-FOLD | ZF | 25.21 ± 3.13 | 0.81 ± 0.02 | 3.01 ± 1.87 | 27.31 ± 3.23 | 0.84 ± 0.02 | 0.21 ± 0.15 | 0.05 ± 0.01 |

L1-ESPIRiT | 27.69 ± 2.79 | 0.62 ± 0.11 | 1.81 ± 1.16 | 27.87 ± 0.78 | 0.70 ± 0.03 | 1.54 ± 0.46 | 143.01 ± 1.13 | |

VN | 30.30 ± 2.88 | 0.85 ± 0.07 | 1.32 ± 1.10 | 30.72 ± 2.31 | 0.87 ± 0.02 | 1.12 ± 0.51 | 0.38 ± 0.00 | |

ZF-GAN | 31.79 ± 2.95 | 0.86 ± 0.03 | 1.11 ± 1.06 | 32.95 ± 2.57 | 0.89 ± 0.02 | 0.92 ± 0.64 | 0.36 ± 0.00 | |

PIC-GAN | 34.99 ± 2.09 | 0.89 ± 0.03 | 0.51 ± 0.27 | 33.20 ± 2.82 | 0.90 ± 0.02 | 0.92 ± 0.63 | 0.69 ± 0.01 | |

6-FOLD | ZF | 24.71 ± 3.31 | 0.79 ± 0.03 | 3.34 ± 2.18 | 25.15 ± 3.37 | 0.79 ± 0.03 | 0.31 ± 0.21 | 0.05 ± 0.01 |

L1-ESPIRiT | 25.40 ± 1.88 | 0.66 ± 0.02 | 2.49 ± 1.04 | 25.71 ± 2.94 | 0.67 ± 0.01 | 2.49 ± 1.30 | 143.43 ± 2.18 | |

VN | 29.26 ± 2.98 | 0.84 ± 0.04 | 1.87 ± 1.28 | 20.76 ± 2.64 | 0.84 ± 0.01 | 1.54 ± 0.97 | 0.39 ± 0.01 | |

ZF-GAN | 31.45 ± 4.00 | 0.85 ± 0.06 | 1.93 ± 1.41 | 30.91 ± 2.72 | 0.85 ± 0.02 | 1.42 ± 1.01 | 0.40 ± 0.00 | |

PIC-GAN | 34.43 ± 1.92 | 0.87 ± 0.05 | 0.58 ± 0.37 | 31.76 ± 3.04 | 0.86 ± 0.02 | 1.22 ± 0.97 | 0.68 ± 0.01 |

**Table 2.**Performance comparisons (NMSE $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-5}$, SSIM, PSNR and Average Reconstruction Time(s)) on knee MRI data with different acceleration factors. The bold numbers highlight the best results. The PIC-GAN outperformed the competing algorithms with significantly higher PSNR, SSIM and lower NMSE values (p < 0.05).

R | METHOD | REGULAR | RANDOM | TIME (s) | ||||
---|---|---|---|---|---|---|---|---|

PSNR | SSIM | NMSE | PSNR | SSIM | NMSE | |||

2-FOLD | ZF | 25.95 ± 1.42 | 0.83 ± 0.03 | 5.25 ± 1.21 | 25.94 ± 1.19 | 0.83 ± 0.01 | 5.28 ± 1.13 | 0.02 ± 0.01 |

L1-ESPIRiT | 31.60 ± 1.27 | 0.72 ± 0.01 | 0.89 ± 0.55 | 30.07 ± 1.00 | 0.73 ± 0.02 | 1.01 ± 0.61 | 67.18 ± 1.10 | |

VN | 32.79 ± 1.42 | 0.85 ± 0.02 | 0.60 ± 0.12 | 32.54 ± 1.43 | 0.86 ± 0.01 | 0.57 ± 0.12 | 0.19 ± 0.01 | |

ZF-GAN | 34.71 ± 1.31 | 0.86 ± 0.00 | 0.44 ± 0.08 | 34.45 ± 1.60 | 0.87 ± 0.00 | 0.39 ± 0.10 | 0.22 ± 0.01 | |

PIC-GAN | 37.80 ± 1.02 | 0.91 ± 0.00 | 0.33 ± 0.09 | 37.98 ± 1.02 | 0.91 ± 0.00 | 0.10 ± 0.02 | 0.43 ± 0.01 | |

4-FOLD | ZF | 24.27 ± 1.41 | 0.78 ± 0.03 | 8.05 ± 1.89 | 24.21 ± 1.23 | 0.78 ± 0.02 | 8.04 ± 1.89 | 0.02 ± 0.00 |

L1-ESPIRiT | 30.67 ± 1.38 | 0.59 ± 0.07 | 1.12 ± 0.57 | 28.98 ± 1.27 | 0.60 ± 0.01 | 1.27 ± 0.22 | 66.12 ± 1.13 | |

VN | 31.65 ± 1.31 | 0.84 ± 0.02 | 0.82 ± 0.21 | 31.23 ± 1.26 | 0.83 ± 0.01 | 0.92 ± 0.20 | 0.19 ± 0.01 | |

ZF-GAN | 33.28 ± 1.27 | 0.85 ± 0.01 | 0.69 ± 0.19 | 33.10 ± 1.26 | 0.84 ± 0.01 | 0.73 ± 0.17 | 0.21 ± 0.01 | |

PIC-GAN | 36.49 ± 1.30 | 0.89 ± 0.01 | 0.46 ± 0.15 | 36.17 ± 0.94 | 0.88 ± 0.01 | 0.58 ± 0.12 | 0.44 ± 0.01 | |

6-FOLD | ZF | 23.18 ± 1.45 | 0.75 ± 0.04 | 8.09 ± 1.91 | 22.44 ± 1.46 | 0.76 ± 0.04 | 8.98 ± 2.31 | 0.02 ± 0.00 |

L1-ESPIRiT | 28.01 ± 0.98 | 0.55 ± 0.00 | 1.28 ± 0.24 | 27.52 ± 1.09 | 0.57 ± 0.01 | 1.59 ± 0.10 | 66.02 ± 1.76 | |

VN | 30.01 ± 1.01 | 0.81 ± 0.01 | 1.18 ± 0.31 | 28.54 ± 1.22 | 0.80 ± 0.00 | 0.98 ± 0.10 | 0.20 ± 0.01 | |

ZF-GAN | 31.47 ± 1.05 | 0.82 ± 0.01 | 0.93 ± 0.29 | 30.48 ± 1.24 | 0.81 ± 0.01 | 0.86 ± 0.11 | 0.24 ± 0.01 | |

PIC-GAN | 34.10 ± 1.09 | 0.86 ± 0.01 | 0.80 ± 0.26 | 33.85 ± 1.11 | 0.85 ± 0.00 | 0.81 ± 0.10 | 0.45 ± 0.01 |

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**MDPI and ACS Style**

Lv, J.; Wang, C.; Yang, G. PIC-GAN: A Parallel Imaging Coupled Generative Adversarial Network for Accelerated Multi-Channel MRI Reconstruction. *Diagnostics* **2021**, *11*, 61.
https://doi.org/10.3390/diagnostics11010061

**AMA Style**

Lv J, Wang C, Yang G. PIC-GAN: A Parallel Imaging Coupled Generative Adversarial Network for Accelerated Multi-Channel MRI Reconstruction. *Diagnostics*. 2021; 11(1):61.
https://doi.org/10.3390/diagnostics11010061

**Chicago/Turabian Style**

Lv, Jun, Chengyan Wang, and Guang Yang. 2021. "PIC-GAN: A Parallel Imaging Coupled Generative Adversarial Network for Accelerated Multi-Channel MRI Reconstruction" *Diagnostics* 11, no. 1: 61.
https://doi.org/10.3390/diagnostics11010061