# End-to-End SAR Deep Learning Imaging Method Based on Sparse Optimization

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## Abstract

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## 1. Introduction

- In order to solve the problems of low imaging quality, excessive parameter settings and difficulty in parameter tuning of traditional SAR sparse imaging methods, we proposed a novel end-to-end SAR sparse imaging method based on a neural network.
- The algorithm only performs imaging processing in the two-dimensional data domain and derives it into a neural network imaging model based on iteration soft threshold algorithm (ISTA) sparse algorithm, instead of arranging two-dimensional echo data into a vector to continuously construct an observation matrix. This can greatly reduce the computational cost and make sparse imaging of large-scale scenes possible.
- Compared with the previous methods, which can only reconstruct simple targets of simulated data and smaller scenes, our algorithm is superior to the traditional sparse algorithm in terms of imaging quality, imaging time, and parameter numbers through simulation data and measured data of three kinds of targets.

## 2. SAR Sparse Imaging Model

#### 2.1. SAR Sparse Imaging Model

#### 2.2. SAR Complex Signal Sparse Imaging Based on a Real-Value Model

#### 2.3. Iterative Optimization of the Sparse Imaging Model Based on L1 Decoupling

## 3. SAR Deep Learning Imaging Method Based on ISTA

#### 3.1. Construction of the Deep Learning Imaging Network

#### 3.2. Training the Deep Learning Imaging Network

**N**is the number of samples. If the mean square error loss function is used, the cost function can be written as

## 4. Experiments and Analysis

#### 4.1. Simulation Point Target Imaging Experiment

#### 4.2. Measured Target Imaging Experiment

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Point target imaging results. (

**a**) is original point target, (

**b**) is Range Doppler method, (

**c**) is our proposed method with L = 3, (

**d**) is our proposed method with L = 8, (

**e**) is our proposed method with L = 11, (

**f**) is ISTA method and (

**g**) is Fast ISTA method.

**Figure 4.**T72 imaging results. (

**a**) is original vehicle target, (

**b**) is our proposed method with L = 3, (

**c**) is our proposed method with L = 8, (

**d**) is our proposed method with L = 11, (

**e**) is ISTA method and (

**f**) is Fast ISTA method.

**Figure 5.**ZSU-23–4 imaging results. (

**a**) is original vehicle target, (

**b**) is our proposed method with L = 3, (

**c**) is our proposed method with L = 8, (

**d**) is our proposed method with L = 11, (

**e**) is ISTA method and (

**f**) is Fast ISTA method.

**Figure 6.**Ship targets on the sea imaging results. (

**a**) is original ship target, (

**b**) is our proposed method with L = 3, (

**c**) is our proposed method with L = 8, (

**d**) is our proposed method with L = 11, (

**e**) is ISTA method and (

**f**) is Fast ISTA method.

**Figure 7.**Inshore ship target imaging results. (

**a**) is original ship target, (

**b**) is our proposed method with L = 3, (

**c**) is our proposed method with L = 8, (

**d**) is our proposed method with L = 11, (

**e**) is ISTA method and (

**f**) is Fast ISTA method.

**Figure 8.**Plane target imaging results. (

**a**) is original plane target, (

**b**) is our proposed method with L = 3, (

**c**) is our proposed method with L = 8, (

**d**) is our proposed method with L = 11, (

**e**) is ISTA method and (

**f**) is Fast ISTA method.

**Figure 9.**Plane target imaging results. (

**a**) is original plane target, (

**b**) is our proposed method with L = 3, (

**c**) is our proposed method with L = 8, (

**d**) is our proposed method with L = 11, (

**e**) is ISTA method and (

**f**) is Fast ISTA method.

Symbol | Quantity | Value |
---|---|---|

${f}_{c}$ | Carrier frequency | 10 GHz |

${B}_{r}$ | Bandwidth | 150 MHz |

PRF | Pulse repetition frequency | 500 Hz |

${T}_{r}$ | Pulse duration | 1.2 $\mathsf{\mu}\mathrm{s}$ |

${\rho}_{r}$ | Range resolution | 2 m |

${\rho}_{a}$ | Azimuth resolution | 2 m |

H | SAR platform altitude | 10,000 m |

V | SAR platform velocity | 100 m/s |

Algorithm | PSNR | NMES | PLSR | Imaging Time |
---|---|---|---|---|

L = 3 | 21.24 dB | 0.52 | −13.68 dB | 0.02s |

L = 8 | 32.68 dB | 0.46 | −16.78 dB | 0.06s |

L = 11 | 34.54 dB | 0.53 | −16.78 dB | 0.25s |

Range Doppler | 22.65 dB | 0.64 | −16.90 dB | 2.56s |

ISTA | 23.70 dB | 0.74 | −14.25 dB | 4.32s |

Fast ISTA | 34.85 dB | 0.92 | −10.65 dB | 2.84s |

Algorithm | Ground Observation Scene | Sea Surface Observation Scene | Ground Airport Observation Scene |
---|---|---|---|

L = 3 | 0.10 s | 0.54 s | 0.98 s |

L = 8 | 0.12 s | 0.68 s | 1.10 s |

L = 11 | 0.12 s | 0.60 s | 1.06 s |

ISTA | 8.67 s | 12.30 s | 14.50 s |

Fast ISTA | 8.10 s | 11.84 s | 13.96 s |

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**MDPI and ACS Style**

Zhao, S.; Ni, J.; Liang, J.; Xiong, S.; Luo, Y.
End-to-End SAR Deep Learning Imaging Method Based on Sparse Optimization. *Remote Sens.* **2021**, *13*, 4429.
https://doi.org/10.3390/rs13214429

**AMA Style**

Zhao S, Ni J, Liang J, Xiong S, Luo Y.
End-to-End SAR Deep Learning Imaging Method Based on Sparse Optimization. *Remote Sensing*. 2021; 13(21):4429.
https://doi.org/10.3390/rs13214429

**Chicago/Turabian Style**

Zhao, Siyuan, Jiacheng Ni, Jia Liang, Shichao Xiong, and Ying Luo.
2021. "End-to-End SAR Deep Learning Imaging Method Based on Sparse Optimization" *Remote Sensing* 13, no. 21: 4429.
https://doi.org/10.3390/rs13214429