# Nonlocal Feature Selection Encoder–Decoder Network for Accurate InSAR Phase Filtering

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Review and Analysis

#### 2.1. Phase Noise Model

#### 2.2. Problem Analysis

## 3. Proposed Method

#### 3.1. Nonlocal Phase Filtering Network

#### 3.1.1. Encoder–Decoder Structure

#### 3.1.2. Neural Nearest Neighbors Block

#### 3.2. Data Generation

#### 3.3. Loss Function

#### 3.4. Performance Evaluation

## 4. Results

#### 4.1. Experiments on Simulated InSAR Data

#### 4.2. Experiments on Real InSAR Data

## 5. Discussion

#### 5.1. Comparison Experiments on Simulated InSAR Data

#### 5.2. Comparison Experiments on Real InSAR Data

#### 5.3. Generalization Ability to Real InSAR Data

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The overall architecture of NL-PFNet. Given the input of the embedding network is Y, the embedding network outputs a pairwise distance matrix D between the query element and nonlocal elements in Y, and a temperature matrix T for each element.

**Figure 3.**Training data: (

**a**) reference DEM; (

**b**) ideal interferometric phase simulated by Figure 3a; (

**c**) noisy interferometric phase with a coherence of 0.75; (

**d**) noisy interferometric phase with a coherence of 0.5.

**Figure 4.**Testing data: (

**a**) reference DEM; (

**b**) ideal interferometric phase simulated by Figure 4a; (

**c**) noisy interferometric phase with a coherence of 0.75; and (

**d**) noisy interferometric phase with a coherence of 0.5.

**Figure 5.**Simulated interferometric phase: (

**a**) clean interferometric phase; (

**b**) noisy version of (

**a**) with a coherence of 0.5.

**Figure 6.**Filtered result and phase error result of the proposed method on simulated data: (

**a**) filtered interferometric phase; and (

**b**) phase error.

**Figure 7.**Real InSAR data and the filtered result using the proposed methods: (

**a**) a real interferometric phase image of Sentinel-1; (

**b**) filtered result.

**Figure 9.**Filtered results (

**top**) and phase error results (

**bottom**) of the four reference methods on simulated data: (

**a**) Lee filter; (

**b**) Goldstein filter; (

**c**) InSAR-BM3D filter; and (

**d**) PFNet.

**Figure 10.**Fitted phase error histogram curves of the five methods. The standard deviation of the six curves are 4.57, 2.45, 1.73, 1.10, 0.68 and 0.62.

**Figure 11.**Quantitative indexes of the proposed and reference methods for phase filtering results on simulated images with different coherences: (

**a**) mean structural similarity index (MSSIM); (

**b**) mean square error (MSE).

**Figure 12.**Filtered results of Figure 7a using the four reference methods: (

**a**) Lee filter; (

**b**) Goldstein filter; (

**c**) InSAR-BM3D filter; and (

**d**) PFNet.

**Figure 13.**Filtered results of a local area in Figure 7a (black rectangle) using the four reference methods: (

**a**) Lee filter; (

**b**) Goldstein filter; (

**c**) InSAR-BM3D filter; and (

**d**) PFNet.

**Figure 14.**Filtered results of a low-coherence area using the proposed and reference methods: (

**a**) a low-coherence area (the white rectangle in Figure 7a); (

**b**) Lee filter; (

**c**) Goldstein filter; (

**d**) InSAR-BM3D filter; (

**e**) PFNet; and (

**f**) proposed method.

**Figure 15.**Filtered results of Figure 15a using the reference and proposed methods: (

**a**) a real interferometric phase image of Sentinel-1 with a different terrain from the training data; (

**b**) Lee filter; (

**c**) Goldstein filter; (

**d**) InSAR-BM3D filter; (

**e**) PFNet; and (

**f**) proposed method.

Block Name | Layer Name | Filter Size | # Channels | Stride | Padding | Output Size |
---|---|---|---|---|---|---|

Encoder block-1 | Conv + Relu | $3\times 3$ | 64 | 1 | 1 | $M\times N\times 64$ |

Conv + BN + Relu | $3\times 3$ | 64 | 1 | 1 | $M/2\times N/2\times 64$ | |

Conv + BN + Relu | $3\times 3$ | 64 | 2 | 1 | $M/2\times N/2\times 64$ | |

Encoder block-2 | Conv + BN + Relu | $3\times 3$ | 128 | 1 | 1 | $M/2\times N/2\times 128$ |

Conv + BN + Relu | $3\times 3$ | 128 | 1 | 1 | $M/2\times N/2\times 128$ | |

Conv + BN + Relu | $3\times 3$ | 128 | 1 | 1 | $M/2\times N/2\times 128$ | |

Encoder block-3 | Conv + BN + Relu | $3\times 3$ | 256 | 1 | 1 | $M/2\times N/2\times 256$ |

Conv + BN + Relu | $3\times 3$ | 256 | 1 | 1 | $M/2\times N/2\times 256$ | |

Conv + BN + Relu | $3\times 3$ | 256 | 1 | 1 | $M/2\times N/2\times 256$ | |

Encoder block-4 | Conv + BN + Relu | $3\times 3$ | 256 | 1 | 1 | $M/2\times N/2\times 256$ |

Conv + BN + Relu | $3\times 3$ | 256 | 1 | 1 | $M/2\times N/2\times 256$ | |

Conv | $3\times 3$ | 8 | 1 | 1 | $M/2\times N/2\times 8$ | |

Neural Nearest Neighbors Block | $M/2\times N/2\times 64$ | |||||

Decoder block-1 | Conv + Relu | $3\times 3$ | 256 | 1 | 1 | $M/2\times N/2\times 256$ |

Conv + BN + Relu | $3\times 3$ | 256 | 1 | 1 | $M/2\times N/2\times 256$ | |

Conv + BN + Relu | $3\times 3$ | 256 | 1 | 1 | $M/2\times N/2\times 256$ | |

Decoder block-2 | Conv + BN + Relu | $3\times 3$ | 128 | 1 | 1 | $M/2\times N/2\times 128$ |

Conv + BN + Relu | $3\times 3$ | 128 | 1 | 1 | $M/2\times N/2\times 128$ | |

Conv + BN + Relu | $3\times 3$ | 128 | 1 | 1 | $M/2\times N/2\times 128$ | |

Decoder block-3 | Conv + BN + Relu | $3\times 3$ | 64 | 1 | 1 | $M/2\times N/2\times 64$ |

Conv + BN + Relu | $3\times 3$ | 64 | 1 | 1 | $M/2\times N/2\times 64$ | |

Conv + BN + Relu | $3\times 3$ | 64 | 1 | 1 | $M/2\times N/2\times 64$ | |

Decoder block-4 | Up + Conv + BN + Relu | $3\times 3$ | 8 | 1 | 1 | $M\times N\times 8$ |

Conv + BN + Relu | $3\times 3$ | 8 | 1 | 1 | $M\times N\times 8$ | |

conv | $3\times 3$ | 2 | 1 | 1 | $M\times N\times 2$ |

Method | NOR | MSSIM | MSE (${\mathbf{Rad}}^{2}$) | $\mathit{T}$ (s) |
---|---|---|---|---|

No filtering | 7217 | 0.074 | 3.47 | - |

Proposed method | 0 | 0.81 | 0.48 | 0.023 |

Method | NOR | PRR (%) | Metric Q | $\mathit{T}\phantom{\rule{0.166667em}{0ex}}\left(\mathit{s}\right)$ |
---|---|---|---|---|

No filtering | 546,647 | 0 | 2.08 | - |

Proposed method | 1624 | 99.70 | 31.70 | 5.35 |

Method | NOR | MSSIM | MSE (${\mathbf{Rad}}^{2}$) | $\mathit{T}$ (s) |
---|---|---|---|---|

Lee filter | 268 | 0.36 | 1.62 | 2.88 |

Goldstein filter | 14 | 0.57 | 1.12 | 2.70 |

InSAR-BM3D filter | 0 | 0.75 | 0.64 | 6.95 |

PFNet | 0 | 0.79 | 0.54 | 0.028 |

Method | NOR | PRR (%) | Metric Q | $\mathit{T}\phantom{\rule{0.166667em}{0ex}}\left(\mathit{s}\right)$ |
---|---|---|---|---|

Lee Filter | 85,930 | 84.28 | 9.93 | 180.26 |

Goldstein Filter | 31,024 | 94.32 | 17.55 | 174.73 |

InSAR-BM3D Filter | 5936 | 98.91 | 25.44 | 483.47 |

PFNet | 415 | 99.92 | 29.02 | 0.25 |

**Table 6.**Quantitative indexes of the proposed and reference methods on a low-coherence area of real InSAR data (the white rectangle in Figure 7a).

Method | NOR | PRR (%) | Metric Q |
---|---|---|---|

No filtering | 11,142 | 0 | 1.80 |

Lee filter | 3011 | 72.98 | 11.17 |

Goldstein filter | 1550 | 86.09 | 17.16 |

InSAR-BM3D filter | 585 | 94.75 | 27.10 |

PFNet | 59 | 99.47 | 32.13 |

Proposed method | 78 | 99.30 | 37.71 |

**Table 7.**Quantitative indexes of the proposed and reference methods on real InSAR data with different terrain from the training data.

Method | NOR | PRR (%) | Metric Q | $\mathit{T}\phantom{\rule{0.166667em}{0ex}}\left(\mathit{s}\right)$ |
---|---|---|---|---|

No filtering | 139,099 | 0 | 1.99 | - |

Lee filter | 19,805 | 85.76 | 10.74 | 44.82 |

Goldstein filter | 6288 | 95.48 | 19.11 | 44.44 |

InSAR-BM3D filter | 893 | 99.36 | 27.65 | 120.11 |

PFNet | 94 | 99.93 | 32.20 | 0.14 |

Proposed method | 113 | 99.92 | 34.17 | 1.37 |

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## Share and Cite

**MDPI and ACS Style**

Pu, L.; Zhang, X.; Zhou, L.; Li, L.; Shi, J.; Wei, S.
Nonlocal Feature Selection Encoder–Decoder Network for Accurate InSAR Phase Filtering. *Remote Sens.* **2022**, *14*, 1174.
https://doi.org/10.3390/rs14051174

**AMA Style**

Pu L, Zhang X, Zhou L, Li L, Shi J, Wei S.
Nonlocal Feature Selection Encoder–Decoder Network for Accurate InSAR Phase Filtering. *Remote Sensing*. 2022; 14(5):1174.
https://doi.org/10.3390/rs14051174

**Chicago/Turabian Style**

Pu, Liming, Xiaoling Zhang, Liming Zhou, Liang Li, Jun Shi, and Shunjun Wei.
2022. "Nonlocal Feature Selection Encoder–Decoder Network for Accurate InSAR Phase Filtering" *Remote Sensing* 14, no. 5: 1174.
https://doi.org/10.3390/rs14051174