A RPCA-Based ISAR Imaging Method for Micromotion Targets
Abstract
:1. Introduction
2. Signal Model and Problem Formulation
- 1.
- Point-scattering model can be satisfied, i.e., the radar echo is assumed to be a sum of dominant scatterers.
- 2.
- The radar echo satisfies the stop–go assumption, i.e., the target is assumed to be static during one pulse duration.
- 3.
- The 2-D imaging plane is unchanged in CPI.
- 4.
- The translational motion is compensated completely, thus, the target is equivalent to rotate around the image center, which indicates that the target can be stated as a turntable model.
- 5.
- The change of aspect angle of the target is so small that the instantaneous range can be approximated by its first-order Taylor expansion.
- 6.
- The range migration among the scatterers is so small that it can be ignored in CPI.
2.1. Signal Model
2.2. Preliminary
2.3. Proposed Optimization Problem
3. Proposed Algorithms
3.1. Algorithm 1
- 1.
- solution for (13)To solve the optimization problem (13), the ADMM method is employed, and the main procedures are derived in the following. For the sake of simplicity, the superscripts and are omitted.To apply the ADMM method, introducing an auxiliary variable and the Lagrange multiplier is required. Then we split the variable as , having the augmented Lagrangian function asProblem (16) involves a quadratic cost and leads to a closed-form solution, which can be obtained by setting the first-order derivative of its objective function with respect to as zero. We obtain
- 2.
- solution for (14)For the problem (14), the splitting variable and the Lagrange multiplier are required. Then we have the augmented Lagrangian function as:Problem (22) has a closed solution, which is represented asThe problem (23) involves a nuclear norm minimization problem, which can be solved by SVT computation in [30]:The whole algorithm is summarized in Algorithm 1 (Micro-doppler Extraction based on RPCA).
Algorithm 1 ME-RPCA. |
|
3.2. Algorithm 2
- 3.
- solution for (28).The augmented Lagrangian form of (28), after simple mathematic manipulation, isObviously, all of the problems associated with (30), (31) and (32) are least squares problems, so that their optimal solutions can be obtained by setting the first-order derivative of corresponding objective functions with respect to the target variables. After some manipulations we haveThe whole algorithm is summarized in Algorithm 2 (Micro-doppler Extraction based on Low Complexity RPCA).
Algorithm 2 ME-LCRPCA. |
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3.3. Convergence Analysis
4. Experiments
5. Conclusions
Author Contributions
Acknowledgments
Conflicts of Interest
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Algorithm 1 | Algorithm 2 | ||
---|---|---|---|
Continuously | Entropy | 1.61 | 1.61 |
sampling | CPU time | 7.1 s | 4.6 s |
Randomly | Entropy | 1.61 | 1.61 |
sampling | CPU time | 7.3 s | 4.7 s |
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Lu, L.; Chen, P.; Wu, L. A RPCA-Based ISAR Imaging Method for Micromotion Targets. Sensors 2020, 20, 2989. https://doi.org/10.3390/s20102989
Lu L, Chen P, Wu L. A RPCA-Based ISAR Imaging Method for Micromotion Targets. Sensors. 2020; 20(10):2989. https://doi.org/10.3390/s20102989
Chicago/Turabian StyleLu, Liangyou, Peng Chen, and Lenan Wu. 2020. "A RPCA-Based ISAR Imaging Method for Micromotion Targets" Sensors 20, no. 10: 2989. https://doi.org/10.3390/s20102989
APA StyleLu, L., Chen, P., & Wu, L. (2020). A RPCA-Based ISAR Imaging Method for Micromotion Targets. Sensors, 20(10), 2989. https://doi.org/10.3390/s20102989