The aim of angular super-resolution is to surpass the real-beam resolution. In this paper, a method for forward-looking scanning radar angular super-resolution imaging through a deconvolution method is proposed, which incorporates the prior information of the target's scattering characteristics. We first mathematically formulate the angular super-resolution problem of forward-looking scanning radar as a maximum a posteriori (MAP) estimation task based on the forward model, and convert it to an equivalent unconstrained optimization problem by applying the log-transforms to the posterior probability, which guarantees the solution converges to a global optimum of an associated MAP problem and it is easy to implement. We then implement the unconstrained optimization task in convex optimization framework using an iterative shrinkage method, and the computational complexity of the proposed algorithm is also discussed. Since the anti log-likelihood of the noise distribution and the prior knowledge of the scene are utilized, the proposed method is able to achieve angular super-resolution imaging in forward-looking scanning radar effectively. Numerical simulations and experimental results based on real data are presented to verify that the proposed deconvolution algorithm has better performance in preserving angular super-resolution accuracy and suppressing the noise amplification.
2. Ramani, S. and J. A. Fessler, "A splitting-based iterative algorithm for accelerated statistical X-ray CT reconstruction," IEEE Transactions on Medical Imaging, Vol. 31, No. 3, 677-688, 2012.
3. Yildirim, S., A. Cemgil, M. Aktar, Y. Ozakin, and A. Ertuzun, "A Bayesian deconvolution approach for receiver function analysis," IEEE Transactions on Geoscience and Remote Sensing, Vol. 48, No. 12, 4151-4163, 2010.
4. Soussen, C., J. Idier, D. Brie, and J. Duan, "From Bernoulli-Gaussian deconvolution to sparse signal restoration," IEEE Transactions on Signal Processing, Vol. 59, No. 10, 4572-4584, 2011.
5. Dickey, F., L. Romero, J. DeLaurentis, and A. Doerry, "Super-resolution, degrees of freedom and synthetic aperture radar," IEE Proceedings - Radar, Sonar and Navigation, Vol. 150, No. 6, 419-429, 2003.
6. Zha, Y., Y. Huang, and J. Yang, "Augmented lagrangian method for angular super-resolution imaging in forward-looking scanning radar," Journal of Applied Remote Sensing, Vol. 9, No. 1, 096055-096055, 2015.
7. Zha, Y., Y. Huang, Z. Sun, Y. Wang, and J. Yang, "Bayesian deconvolution for angular super-resolution in forward-looking scanning radar," Sensors, Vol. 15, No. 3, 6924-6946, 2015.
8. Tello Alonso, M., P. López-Dekker, and J. J. Mallorquí, "A novel strategy for radar imaging based on compressive sensing," IEEE Transactions on Geoscience and Remote Sensing, Vol. 48, No. 12, 4285-4295, 2010.
9. Gambardella, A. and M. Migliaccio, "On the superresolution of microwave scanning radiometer measurements," IEEE Geoscience and Remote Sensing Letters, Vol. 5, No. 4, 796-800, 2008.
10. Uttam, S. and N. A. Goodman, "Superresolution of coherent sources in real-beam data," IEEE Transactions on Aerospace and Electronic Systems, Vol. 46, No. 3, 1557-1566, 2010.
11. Sundareshan, M. K. and S. Bhattacharjee, "Enhanced iterative processing algorithms for restoration and superresolution of tactical sensor imagery," Optical Engineering, Vol. 43, No. 1, 199-208, 2004.
12. Lohner, A., "Improved azimuthal resolution of forward looking SAR by sophisticated antenna illumination function design," IEE Proceedings - Radar, Sonar and Navigation, 128-134, IET, 1998.
13. Xu, Z., X. Chang, F. Xu, and H. Zhang, "L1/2 regularization: A thresholding representation theory and a fast solver," IEEE Transactions on Neural Networks and Learning Systems, Vol. 23, No. 7, 1013-1027, 2012.
14. Ramani, S., Z. Liu, J. Rosen, J. Nielsen, and J. A. Fessler, "Regularization parameter selection for nonlinear iterative image restoration and MRI reconstruction using GCV and SURE-based methods," IEEE Transactions on Image Processing, Vol. 21, No. 8, 3659-3672, 2012.
15. Babacan, S. D., R. Molina, and A. K. Katsaggelos, "Variational Bayesian super resolution," IEEE Transactions on Image Processing, Vol. 20, No. 4, 984-999, 2011.
16. Lane, R., "Non-parametric Bayesian super-resolution," IET Radar, Sonar and Navigation, Vol. 4, No. 4, 639-648, 2010.
17. Richardson, W. H., "Bayesian-based iterative method of image restoration," JOSA, Vol. 62, No. 1, 55-59, 1972.
18. Lucy, L., "An iterative technique for the rectification of observed distributions," The Astronomical Journal, Vol. 79, 745, 1974.
19. White, R. L., "Image restoration using the damped Richardson-Lucy method," The Restoration of HST Images and Spectra II, 104-110, 1994.
20. Mohammad-Djafari, A., "Bayesian approach for inverse problems in optical coherent and noncoherent imaging," SPIE's 48th Annual Meeting on Optical Science and Technology, 209-218, International Society for Optics and Photonics, 2003.
21. Beck, A. and M. Teboulle, "A fast iterative shrinkage-thresholding algorithm for linear inverse problems," SIAM Journal on Imaging Sciences, Vol. 2, No. 1, 183-202, 2009.
22. Figueiredo, M. A. and R. D. Nowak, "An EM algorithm for wavelet-based image restoration," IEEE Transactions on Image Processing, Vol. 12, No. 8, 906-916, 2003.
23. Bioucas-Dias, J. M. and M. A. Figueiredo, "A new twist: Two-step iterative shrinkage/thresholding algorithms for image restoration," IEEE Transactions on Image Processing, Vol. 16, No. 12, 2992-3004, 2007.
24. Combettes, P. L. and V. R. Wajs, "Signal recovery by proximal forward-backward splitting," Multiscale Modeling & Simulation, Vol. 4, No. 4, 1168-1200, 2005.
25. Samadi, S., M. Çetin, and M. A. Masnadi-Shirazi, "Sparse representation-based synthetic aperture radar imaging," IET Radar, Sonar and Navigation, Vol. 5, No. 2, 182-193, 2011.
26. Donoho, D. L., "De-noising by soft-thresholding," IEEE Transactions on Information Theory, Vol. 41, No. 3, 613-627, 1995.
27. Karl, W. C., Regularization in Image Restoration and Reconstruction, Elsevier, New York, 2005.
28. Hansen, P. C., "Analysis of discrete ill-posed problems by means of the L-curve," SIAM Review, Vol. 34, No. 4, 561-580, 1992.
29. Zhang, Y., R. Li, and C. L. Tsai, "Regularization parameter selections via generalized information criterion," Journal of the American Statistical Association, Vol. 105, No. 489, 312-323, 2010.
30. Sourbron, S., R. Luypaert, P. Van Schuerbeek, M. Dujardin, and T. Stadnik, "Choice of the regularization parameter for perfusion quantification with MRI," Physics in Medicine and Biology, Vol. 49, No. 14, 3307, 2004.
31. Huang, Y., M. K. Ng, and Y. W. Wen, "A fast total variation minimization method for image restoration," Multiscale Modeling & Simulation, Vol. 7, No. 2, 774-795, 2008.
32. Figueiredo, M. A. and J. M. Bioucas-Dias, "Restoration of Poissonian images using alternating direction optimization," IEEE Transactions on Image Processing, Vol. 19, No. 12, 3133-3145, 2010.
33. Li, W., J. Yang, and Y. Huang, "Keystone transform-based space-variant range migration correction for airborne forward-looking scanning radar," Electronics Letters, Vol. 48, No. 2, 121-122, 2012.