# Enhanced Millimeter-Wave 3-D Imaging via Complex-Valued Fully Convolutional Neural Network

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Enhanced MMW 3-D Imaging Using CVFCNN

#### 2.1. Framework of Enhanced MMW Imaging via CVFCNN

#### 2.2. Training Process

#### 2.3. Parameter Initialization

## 3. Results

#### 3.1. Numerical Simulations

_{1}-norm and TV-norm. Next, we will provide comparisons of these methods through simulations and experiments.

^{−6}. The parameters of CPReLU and PReLU are initialized to be 0.25 without weight decay, and the learning rate is 6 × 10

^{−4}. We trained for 8 epochs with a batch size of 16. The networks were programmed based on MATLAB, implemented on a computer platform with an Intel Xeon E5-2687W v4 CPU.

_{1}represents the CPReLU demonstrated in [31] with constant parameters, and the parameters are set as the initial value, i.e., 0.25. CPReLU

_{2}refers to the proposed adaptive CPReLU, with independent real and imaginary parameters. Note that the neural network methods outperform both the traditional PSM method and the CS method with respect to different data ratios. The proposed CVFCNN (CPReLU

_{2}) possesses the minimum number of errors among the neural network methods. We also note that the parameters of RVFCNN are twice those of CVFCNN [28]. Specifically, CVFCNN (CPReLU

_{1}) and CVFCNN (CPReLU

_{2}) contain 38,032 real numbers, CVFCNN (CReLU) contains 37,936 real numbers, and RVFCNN (PReLU) contains 75,968 real numbers in this example. However, RVFCNN does not perform better. The CVFCNN (CPReLU

_{1}) has relatively poor performance, which means it is unreliable to directly set a constant value as the parameter of CPReLU

_{1}. Similarly, the performance of CReLU is also inferior to that of CPReLU

_{2}, due to being without adaptive parameter adjustments.

_{2}) is slightly slower than CVFCNN (CReLU) and CVFCNN (CPReLU

_{1}) because the parameters of the CPReLU

_{2}activation function need to be updated adaptively during the training stage. However, in general, people pay more attention to the processing time of the testing stage, as shown in Table 4.

_{2}) on the CPU is slightly longer than that of CVFCNN (CReLU) but with a lower SSE, as shown in Table 2. Usually, in order to obtain a better-quality image, the cost of a little processing time could be ignored. In addition, when processed by the GPU, the processing time difference between CVFCNN (CPReLU

_{2}) and CVFCNN (CReLU) in this simulation experiment is very small, being less than 0.01 s.

#### 3.2. Results of the Measured Data

_{1}(Figure 6f) and CPReLU

_{2}(Figure 6g) are more uniform than those of PReLU (Figure 6d) and CReLU (Figure 6e). Note from the detailed subfigures that the result of the proposed CPReLU

_{2}in Figure 6g exhibits lower sidelobes than the results in Figure 6d–f, respectively, wherein the sidelobes are indicated by red arrows. The experimental results show that the proposed CPReLU

_{2}performs best of the tested methods.

_{2}) is slightly longer than that of CVFCNN (CReLU) but yielded better imaging results, as shown in Figure 6. Usually, in order to obtain a better-quality image, the cost of a little processing time could be ignored.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Casalini, E.; Frioud, M.; Small, D.; Henke, D. Refocusing FMCW SAR Moving Target Data in the Wavenumber Domain. IEEE Trans. Geosci. Remote Sens.
**2019**, 57, 3436–3449. [Google Scholar] [CrossRef] - Wang, H.; Zhang, H.; Dai, S.; Sun, Z. Azimuth Multichannel GMTI Based on Ka-Band DBF-SCORE SAR System. IEEE Geosci. Remote Sens. Lett.
**2018**, 15, 419–423. [Google Scholar] [CrossRef] - Amin, M. Radar for Indoor Monitoring: Detection, Classification, and Assessment; CRC Press: Boca Raton, FL, USA, 2017. [Google Scholar]
- Sheen, D.; McMakin, D.; Hall, T. Near-Field Three-Dimensional Radar Imaging Techniques and Applications. Appl. Opt.
**2010**, 49, 83–93. [Google Scholar] [CrossRef] [PubMed] - Sheen, D.M.; McMakin, D.L.; Hall, T.E. Three-Dimensional Millimeter-Wave Imaging for Concealed Weapon Detection. IEEE Trans. Microw. Theory Tech.
**2001**, 49, 1581–1592. [Google Scholar] [CrossRef] - Oliveri, G.; Salucci, M.; Anselmi, N.; Massa, A. Compressive Sensing as Applied to Inverse Problems for Imaging: Theory, Applications, Current Trends, and Open Challenges. IEEE Antennas Propag. Mag.
**2017**, 59, 34–46. [Google Scholar] [CrossRef] - Rani, M.; Dhok, S.B.; Deshmukh, R.B. A Systematic Review of Compressive Sensing: Concepts, Implementations and Applications. IEEE Access
**2018**, 6, 4875–4894. [Google Scholar] [CrossRef] - Upadhyaya, V.; Salim, D.M. Compressive Sensing: Methods, Techniques, and Applications. IOP Conf. Ser. Mater. Sci. Eng.
**2021**, 1099, 012012. [Google Scholar] [CrossRef] - Seyfioglu, M.S.; Erol, B.; Gurbuz, S.Z.; Amin, M.G. DNN Transfer Learning from Diversified Micro-Doppler for Motion Classification. IEEE Trans. Aerosp. Electron. Syst.
**2019**, 55, 2164–2180. [Google Scholar] [CrossRef][Green Version] - Erol, B.; Gurbuz, S.Z.; Amin, M.G. Motion Classification Using Kinematically Sifted ACGAN-Synthesized Radar Micro-Doppler Signatures. IEEE Trans. Aerosp. Electron. Syst.
**2020**, 56, 3197–3213. [Google Scholar] [CrossRef][Green Version] - Skaria, S.; Al-Hourani, A.; Lech, M.; Evans, R.J. Hand-Gesture Recognition Using Two-Antenna Doppler Radar with Deep Convolutional Neural Networks. IEEE Sens. J.
**2019**, 19, 3041–3048. [Google Scholar] [CrossRef] - Chen, Z.; Li, G.; Fioranelli, F.; Griffiths, H. Dynamic Hand Gesture Classification Based on Multistatic Radar Micro-Doppler Signatures Using Convolutional Neural Network. In Proceedings of the 2019 IEEE Radar Conference (RadarConf), Boston, MA, USA, 22–26 April 2019; pp. 1–5. [Google Scholar]
- Qin, D.; Liu, D.; Gao, X.; Jingkun, G. ISAR Resolution Enhancement Using Residual Network. In Proceedings of the 2019 IEEE 4th International Conference on Signal and Image Processing (ICSIP), Wuxi, China, 19–21 July 2019; pp. 788–792. [Google Scholar]
- Gao, X.; Qin, D.; Gao, J. Resolution Enhancement for Inverse Synthetic Aperture Radar Images Using a Deep Residual Network. Microw. Opt. Technol. Lett.
**2020**, 62, 1588–1593. [Google Scholar] [CrossRef] - Hu, C.; Wang, L.; Li, Z.; Zhu, D. Inverse Synthetic Aperture Radar Imaging Using a Fully Convolutional Neural Network. IEEE Geosci. Remote Sens. Lett.
**2020**, 17, 1203–1207. [Google Scholar] [CrossRef] - Yang, T.; Shi, H.; Lang, M.; Guo, J. ISAR Imaging Enhancement: Exploiting Deep Convolutional Neural Network for Signal Reconstruction. Int. J. Remote Sens.
**2020**, 41, 9447–9468. [Google Scholar] [CrossRef] - Cheng, Q.; Ihalage, A.A.; Liu, Y.; Hao, Y. Compressive Sensing Radar Imaging With Convolutional Neural Networks. IEEE Access
**2020**, 8, 212917–212926. [Google Scholar] [CrossRef] - Mu, H.; Zhang, Y.; Ding, C.; Jiang, Y.; Er, M.H.; Kot, A.C. DeepImaging: A Ground Moving Target Imaging Based on CNN for SAR-GMTI System. IEEE Geosci. Remote Sens. Lett.
**2021**, 18, 117–121. [Google Scholar] [CrossRef] - Pu, W. Shuffle GAN with Autoencoder: A Deep Learning Approach to Separate Moving and Stationary Targets in SAR Imagery. IEEE Trans. Neural Netw. Learn. Syst.
**2021**, 1–15. [Google Scholar] [CrossRef] [PubMed] - Ding, J.; Wen, L.; Zhong, C.; Loffeld, O. Video SAR Moving Target Indication Using Deep Neural Network. IEEE Trans. Geosci. Remote Sens.
**2020**, 58, 7194–7204. [Google Scholar] [CrossRef] - Fang, S.; Nirjon, S. SuperRF: Enhanced 3D RF Representation Using Stationary Low-Cost MmWave Radar. In Proceedings of the International Conference on Embedded Wireless Systems and Networks (EWSN), Lyon, France, 17–19 February 2020; Volume 2020, pp. 120–131. [Google Scholar]
- Sun, Y.; Huang, Z.; Zhang, H.; Cao, Z.; Xu, D. 3DRIMR: 3D Reconstruction and Imaging via MmWave Radar Based on Deep Learning. arXiv
**2021**, arXiv:2108.02858. [Google Scholar] - Guan, J.; Madani, S.; Jog, S.; Gupta, S.; Hassanieh, H. Through Fog High-Resolution Imaging Using Millimeter Wave Radar. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Seattle, WA, USA, 13–19 June 2020. [Google Scholar]
- Gao, J.; Qin, Y.; Deng, B.; Wang, H.; Li, X. A Novel Method for 3-D Millimeter-Wave Holographic Reconstruction Based on Frequency Interferometry Techniques. IEEE Trans. Microw. Theory Tech.
**2018**, 66, 1579–1596. [Google Scholar] [CrossRef] - Minin, I.V.; Minin, O.V.; Castineira-Ibanez, S.; Rubio, C.; Candelas, P. Phase Method for Visualization of Hidden Dielectric Objects in the Millimeter Waveband. Sensors
**2019**, 19, 3919. [Google Scholar] [CrossRef] [PubMed][Green Version] - Sadeghi, M.; Tajdini, M.M.; Wig, E.; Rappaport, C.M. Single-Frequency Fast Dielectric Characterization of Concealed Body-Worn Explosive Threats. IEEE Trans. Antennas Propag.
**2020**, 68, 7541–7548. [Google Scholar] [CrossRef] - Aizenberg, N.N.; Ivaskiv, Y.L.; Pospelov, D.A.; Hudiakov, G.F. Multivalued Threshold Functions in Boolean Complex-Threshold Functions and Their Generalization. Cybern. Syst. Anal.
**1971**, 7, 626–635. [Google Scholar] [CrossRef] - Hirose, A. Complex-Valued Neural Networks: Advances and Applications; Wiley: New York, NY, USA, 2013. [Google Scholar]
- Trabelsi, C.; Bilaniuk, O.; Zhang, Y.; Serdyuk, D.; Subramanian, D.; Santos, J.F.; Mehri, S.; Rostamzadeh, N.; Bengio, Y.; Pal, C.J. Deep Complex Networks. In Proceedings of the ICLR 2018 Conference, Vancouver, BC, Canada, 30 April–3 May 2018. [Google Scholar]
- Gao, J.; Deng, B.; Qin, Y.; Wang, H.; Li, X. Enhanced Radar Imaging Using a Complex-Valued Convolutional Neural Network. IEEE Geosci. Remote Sens. Lett.
**2019**, 16, 35–39. [Google Scholar] [CrossRef][Green Version] - Zhang, Y.; Yang, Q.; Zeng, Y.; Deng, B.; Wang, H.; Qin, Y. High-Quality Interferometric Inverse Synthetic Aperture Radar Imaging Using Deep Convolutional Networks. Microw. Opt. Technol. Lett.
**2020**, 62, 3060–3065. [Google Scholar] [CrossRef] - Pu, W. Deep SAR Imaging and Motion Compensation. IEEE Trans. Image Process.
**2021**, 30, 2232–2247. [Google Scholar] [CrossRef] [PubMed] - Mu, H.; Zhang, Y.; Jiang, Y.; Ding, C. CV-GMTINet: GMTI Using a Deep Complex-Valued Convolutional Neural Network for Multichannel SAR-GMTI System. IEEE Trans. Geosci. Remote Sens.
**2022**, 60, 5201115. [Google Scholar] [CrossRef] - Shelhamer, E.; Long, J.; Darrell, T. Fully Convolutional Networks for Semantic Segmentation. IEEE Trans. Pattern Anal. Mach. Intell.
**2017**, 39, 640–651. [Google Scholar] [CrossRef] - Sutskever, I.; Martens, J.; Dahl, G.; Hinton, G. On the Importance of Initialization and Momentum in Deep Learning. In Proceedings of the 30th International Conference on International Conference on Machine Learning, Atlanta, GA, USA, 16–21 June 2013. [Google Scholar]
- Bengio, Y. Practical recommendations for gradient-based training of deep architectures. In Neural Networks: Tricks of the Trade; Springer: Berlin/Heidelberg, Germany, 2012; pp. 437–478. [Google Scholar]
- Li, S.; Zhao, G.; Sun, H.; Amin, M. Compressive Sensing Imaging of 3-D Object by a Holographic Algorithm. IEEE Trans. Antennas Propag.
**2018**, 66, 7295–7304. [Google Scholar] [CrossRef] - Yang, G.; Li, C.; Wu, S.; Liu, X.; Fang, G. MIMO-SAR 3-D Imaging Based on Range Wavenumber Decomposing. IEEE Sens. J.
**2021**, 21, 24309–24317. [Google Scholar] [CrossRef] - Gao, H.; Li, C.; Zheng, S.; Wu, S.; Fang, G. Implementation of the Phase Shift Migration in MIMO-Sidelooking Imaging at Terahertz Band. IEEE Sens. J.
**2019**, 19, 9384–9393. [Google Scholar] [CrossRef] - Tan, W.; Huang, P.; Huang, Z.; Qi, Y.; Wang, W. Three-Dimensional Microwave Imaging for Concealed Weapon Detection Using Range Stacking Technique. Int. J. Antennas Propag.
**2017**, 2017, 1480623. [Google Scholar] [CrossRef][Green Version]

**Figure 3.**Active regions of different activation functions: (

**a**) CReLU; (

**b**) CPReLU [31]; (

**c**) proposed CPReLU.

**Figure 4.**Structures of enhanced MMW 3-D imaging: (

**a**) the proposed CVFCNN (CPReLU); (

**b**) RVFCNN (PReLU); (

**c**) CVFCNN (CReLU); (

**d**) operator-based CS.

**Figure 6.**Images showing the 2-D images using 50% of data: (

**a**) the measured targets; (

**b**) image via PSM; (

**c**) image via CS; (

**d**) image via RVFCNN (PReLU); (

**e**) image via CVFCNN (CReLU); (

**f**) image via CVFCNN (CPReLU

_{1}); (

**g**) image via CVFCNN (CPReLU

_{2}).

Parameter | Value |
---|---|

Frequency (GHz) | 34.5 |

Aperture size (m) | 0.25 × 0.25 |

Sampling interval (mm) | 5 |

Imaging range (m) | 0.25 m~0.45 m |

Beam width of antenna element (°) | 55 |

Original resolution (mm) | 5 |

Enhanced imaging resolution (mm) | 2.5 |

Image pixels | 256 × 256 |

Methods | 25% Data | 50% Data | 75% Data | 100% Data |
---|---|---|---|---|

PSM | 1214.51 | 653.47 | 392.01 | 261.44 |

PSM-CS | 142.37 | 62.65 | 56.93 | 55.84 |

RVFCNN (PReLU) | 83.57 | 58.54 | 47.82 | 39.68 |

CVFCNN (CReLU) | 83.82 | 59.14 | 48.02 | 39.93 |

CVFCNN (CPReLU_{1}) | 84.87 | 61.39 | 50.47 | 42.67 |

CVFCNN (CPReLU_{2}) | 82.74 | 58.21 | 47.18 | 39.19 |

Methods | CPU(h) |
---|---|

RVFCNN (PReLU) | 22.6 |

CVFCNN (CReLU) | 13.3 |

CVFCNN (CPReLU_{1}) | 15.2 |

CVFCNN (CPReLU_{2}) | 15.4 |

Methods | CPU(s) | GPU(s) |
---|---|---|

PSM | 0.12 | / |

PSM-CS | 22.82 | / |

RVFCNN (PReLU) | 1.18 | 0.10 |

CVFCNN (CReLU) | 0.71 | 0.08 |

CVFCNN (CPReLU_{1}) | 0.72 | 0.08 |

CVFCNN (CPReLU_{2}) | 0.72 | 0.08 |

Parameter | Value |
---|---|

Center frequency (GHz) | 34.5 |

Bandwidth (GHz) | 5 |

Sampling interval (mm) | Δx = 4, Δy = 5 |

Beam width of antenna element (°) | 55 |

Imaging range (m) | 0.3 m~0.42 m |

Imaging range interval (mm) | 5 |

Imaging range slices | 25 |

Image pixels | 768 × 768 |

Methods | CPU(s) | GPU(s) |
---|---|---|

PSM | 4.5 | / |

PSM-CS | 647.2 | / |

RVFCNN (PReLU) | 240.2 | 16.4 |

CVFCNN (CReLU) | 143.6 | 11.9 |

CVFCNN (CPReLU_{1}) | 145.3 | 12.2 |

CVFCNN (CPReLU_{2}) | 145.3 | 12.2 |

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**MDPI and ACS Style**

Jing, H.; Li, S.; Miao, K.; Wang, S.; Cui, X.; Zhao, G.; Sun, H.
Enhanced Millimeter-Wave 3-D Imaging via Complex-Valued Fully Convolutional Neural Network. *Electronics* **2022**, *11*, 147.
https://doi.org/10.3390/electronics11010147

**AMA Style**

Jing H, Li S, Miao K, Wang S, Cui X, Zhao G, Sun H.
Enhanced Millimeter-Wave 3-D Imaging via Complex-Valued Fully Convolutional Neural Network. *Electronics*. 2022; 11(1):147.
https://doi.org/10.3390/electronics11010147

**Chicago/Turabian Style**

Jing, Handan, Shiyong Li, Ke Miao, Shuoguang Wang, Xiaoxi Cui, Guoqiang Zhao, and Houjun Sun.
2022. "Enhanced Millimeter-Wave 3-D Imaging via Complex-Valued Fully Convolutional Neural Network" *Electronics* 11, no. 1: 147.
https://doi.org/10.3390/electronics11010147