# Characterization and Removal of RFI Artifacts in Radar Data via Model-Constrained Deep Learning Approach

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Background and Motivation

#### 1.2. Related Works

#### 1.3. Contributions

- (1)
- This paper established a joint low−rank and sparse optimization framework by considering the temporalspatial correlation of target response, as well as the random sparsity property for time−varying interference. The model−based iterative optimization procedures are derived and propose an alternative recurrent neural networks (RNN) structure to imitate the iterative process, which improves the efficiency and provides an innovative insight into the traditional iterative optimization problems.
- (2)
- In the proposed hybrid fusing scheme, the original unsupervised decomposition problem is equivalently converted to a supervised neural network−based learning problem. Unlike the generic off−the−shelf network structure, such a strategy incorporates partial domain knowledge via the underlying physical modeling into the network architecture. The model constrained network architecture is more interpretable, and the hyperparameters could be learned from reasonably sized training sets, rather than predefined through empirically manual tuning.
- (3)
- The performance of the proposed method is verified on simulated and real measured experimental results under complicated heterogeneous scenarios with typical RFI types. It could achieve a better balance between efficiency and accuracy, which is beneficial for incorporation into the general automated processing flow of SAR data processing.

## 2. Problem Formulation

_{r}denotes the samples along fast-time.

**H**

_{1}and

**H**

_{2}are the measurement matrices of appropriate dimensions.

**E**denotes the noise matrix. Figure 4 illustrates the physical model establishment process which incorporates the prior domain knowledge.

**5**).

## 3. Theory and Methodology

## 4. Experimental Results and Discussions

#### 4.1. Experimental Results of Synthetic Data

#### 4.1.1. Experimental Setting

#### 4.1.2. Performance Discussion

#### 4.2. Experimental Results of Real−Measured Data

## 5. Conclusions

- (1)
- From the data modeling perspective, the problem is formulated by principled physical modeling. Considering the spatial-temporal correlation between adjacent pulses, as well as the time-varying property of RFI, the problem is modelled as a joint low-rank and sparse decomposition issue. The original solution is achieved via unsupervised iterative optimization, in which the regularization parameters should be set as a priori and the convergence rate is not explicitly guaranteed.
- (2)
- From the data characterization perspective, the proposed hybrid framework incorporates the recurrent neural network units to imitate the iterative process. By employing this replacement, the proposed hybrid framework can perform automatic tuning of hyperparameters, speed up the efficiency, and increase the interpretability of the network.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Comparison of SAR images with and without RFI artifacts acquired by the European Sentinel−1 system. The obvious artifacts in (

**a**,

**b**) are terrestrial interference, while in (

**c**,

**d**) they represent inter−satellite mutual interference.

**Figure 6.**The architecture of the proposed model−constrained deep learning approach. (

**a**) Original iterative optimization problem. (

**b**) Proposed equivalent replacement of stacked multi−layer RNN units.

**Figure 9.**Comparison results of two particular sub−blocks for the narrowband RFI. (

**a**) Original RFI−free spectrogram, (

**b**) Simulated RFI, (

**c**) RFI−contaminated spectrogram. (

**d**) Estimated target response. (

**e**) Extracted interference patterns. Each row corresponds to a particular pulse.

**Figure 10.**Comparison results of two particular sub−blocks for the pulsed RFI. (

**a**) Original RFI−free spectrogram, (

**b**) Simulated RFI, (

**c**) RFI−contaminated spectrogram. (

**d**) Estimated target response. (

**e**) Extracted interference patterns. Each row corresponds to a particular pulse.

**Figure 11.**Comparison results of two particular sub−blocks for the chirp modulated RFI. (

**a**) Original RFI−free spectrogram, (

**b**) Simulated RFI, (

**c**) RFI−contaminated spectrogram. (

**d**) Estimated target response. (

**e**) Extracted interference patterns. Each row corresponds to a particular pulse.

**Figure 12.**Comparison results for narrowband RFI with strong energy. (

**a**) depicts the echoes for processing. (

**b**–

**d**) are the results of PCA, RPCA, and the proposed approach, respectively.

**Figure 13.**Comparison results for pulsed RFI with strong energy. (

**a**) depicts the echoes for processing. (

**b**–

**d**) are the results of PCA, RPCA, and the proposed approach, respectively.

**Figure 14.**Comparison results for chirp modulated RFI with weak energy. (

**a**) depicts the echoes for processing. (

**b**–

**d**) are the results of PCA, RPCA, and the proposed approach, respectively.

**Figure 15.**Comparison results for sinusoidal modulated RFI with weak energy. (

**a**) depicts the echoes for processing. (

**b**–

**d**) are the results of PCA, RPCA, and the proposed approach, respectively.

**Figure 16.**Simulated echoes for performance verification. (

**a**) Original RFI−free spectrogram, (

**b**) Simulated RFI, (

**c**) RFI−contaminated spectrograms.

**Figure 17.**Comparison results after applying (

**a**) PCA, (

**b**) BSF, (

**c**) RPCA, and (

**d**) the proposed approach.

**Figure 19.**Comparison of imaging results. (

**a**) RFI-contaminated image. (

**b**) PCA, (

**c**) BSF, (

**d**) RPCA, and (

**e**) proposed method.

**Figure 20.**Zoomed up results of the imaging results produced by (

**a**) PCA, (

**b**) BSF, (

**c**) RPCA, and (

**d**) proposed method.

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**MDPI and ACS Style**

Tao, M.; Li, J.; Su, J.; Wang, L.
Characterization and Removal of RFI Artifacts in Radar Data via Model-Constrained Deep Learning Approach. *Remote Sens.* **2022**, *14*, 1578.
https://doi.org/10.3390/rs14071578

**AMA Style**

Tao M, Li J, Su J, Wang L.
Characterization and Removal of RFI Artifacts in Radar Data via Model-Constrained Deep Learning Approach. *Remote Sensing*. 2022; 14(7):1578.
https://doi.org/10.3390/rs14071578

**Chicago/Turabian Style**

Tao, Mingliang, Jieshuang Li, Jia Su, and Ling Wang.
2022. "Characterization and Removal of RFI Artifacts in Radar Data via Model-Constrained Deep Learning Approach" *Remote Sensing* 14, no. 7: 1578.
https://doi.org/10.3390/rs14071578