Sparse Regularization with a Non-Convex Penalty for SAR Imaging and Autofocusing
Abstract
:1. Introduction
2. SAR Data Acquisition Model
3. The Proposed CFBA Method
3.1. The Optimization Model
3.2. Complex Forward-Backward Splitting-Based Method
3.2.1. Image Reconstruction Step
3.2.2. Optimization of the Phase Errors
Algorithm 1: CFBA |
3.3. Convergence Analysis
3.3.1. Convergence of the Inner Complex Forward-Backward Splitting Algorithm
3.3.2. Convergence of the Outer Alternating Minimization Method
4. Wirtinger Alternating Minimization Autofocusing
4.1. The Original Method
Algorithm 2: WAMA |
4.2. Extension to Several Other Regularizers
- (1)
- The pth power of an approximate normIn this case,This yields the same algorithm as in this case of [12], but no reference to the literature of Wirtinger calculus is made therein. Therefore, this deduction can be viewed as an alternative perspective to interpret SDA;
- (2)
- Approximate total variationFor approximate total variation, the situation is more complicated. However, the result can still be incorporated in the form of (47). Let be the 2D matrix form of the N-dimensional vector ; thenNowAs for , and , they are matrices that contain only 0, 1, and −1 and are constructed so that they realize the following relations:
- (3)
- Welsh potential
- (4)
- Geman–McClure potentialIn this case, another variant of regularization [42] is imposed on the magnitude of f, and we have
4.3. Convergence Analysis
- 1.
- Find by
- 2.
- Find byThis leads to:
- 3.
- Find byThis leads to:
5. Experimental Results
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. The Proof of Lemma 1
Appendix B. Another Proof of Theorem 1
References
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Carrier Frequency | |
Chirp Rate | |
Pulse Duration | |
Angular Range | ° |
MSE | |||||
---|---|---|---|---|---|
Method | Scene 1 | Scene 2 | Scene 3 | Scene 4 | Scene 5 |
SDA | 5.4310 | 6.4964 | 6.3576 | 1.3997 | 6.8909 |
WAMA | 1.2227 | 6.3029 | 5.3663 | 2.2250 | 7.8785 |
CFBA | 1.1836 | 6.2940 | 5.4803 | 1.3483 | 6.5628 |
Entropy | |||||
Method | Scene 1 | Scene 2 | Scene 3 | Scene 4 | Scene 5 |
SDA | 1.4621 | 5.4410 | 5.6918 | 4.5720 | 4.2847 |
WAMA | 0.3327 | 5.4333 | 5.6641 | 4.5230 | 4.2782 |
CFBA | 0.3430 | 5.4228 | 5.6602 | 4.5617 | 4.2916 |
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Zhang, Z.-Y.; Pappas, O.; Rizaev, I.G.; Achim, A. Sparse Regularization with a Non-Convex Penalty for SAR Imaging and Autofocusing. Remote Sens. 2022, 14, 2190. https://doi.org/10.3390/rs14092190
Zhang Z-Y, Pappas O, Rizaev IG, Achim A. Sparse Regularization with a Non-Convex Penalty for SAR Imaging and Autofocusing. Remote Sensing. 2022; 14(9):2190. https://doi.org/10.3390/rs14092190
Chicago/Turabian StyleZhang, Zi-Yao, Odysseas Pappas, Igor G. Rizaev, and Alin Achim. 2022. "Sparse Regularization with a Non-Convex Penalty for SAR Imaging and Autofocusing" Remote Sensing 14, no. 9: 2190. https://doi.org/10.3390/rs14092190