In order to improve the reconstruction accuracy of near-field SAIR, a novel regularization imaging algorithm based on an accurate G matrix is proposed in this paper. Due to the fact that the regularization reconstruction is usually an underdetermined problem, inaccurate operation matrix G will lead to great reconstruction error in the imaging results, or even the normal imaging cannot be obtained. In this paper, we establish an accurate G matrix based on the accurate imaging model of near-field SAIR. Compared with the traditional G matrix with some unnecessary approximations, the proposed G matrix without approximation can improve the reconstruction accuracy effectively. For improving the accuracy of matrix G further, the corresponding parameters are corrected according to the RMSE between the imaging results of the regularization method and modified FFT method which is not sensitive to the parameters' change. The effectiveness of this calibration method has been tested by 1D simulation experiments. Moreover, the 2D simulation experiments demonstrate that the proposed accurate G matrix can improve the imaging accuracy of regularization method effectively. Finally, the 1D imaging experiment is performed to test the effectiveness of the proposed method for the actual synthetic aperture imaging further.
1. Appleby, R. and R. N. Anderton, "Millimeter-wave and submillimeter-wave imaging for security and surveillance," Proceedings of the IEEE, Vol. 95, No. 8, 1683-1690, Aug. 200. doi:10.1109/JPROC.2007.898832
2. Sheen, M. D., D. L. McMakin, and T. E. Hall, "Three-dimensional millimeter-wave imaging for concealed weapon detection," IEEE Trans. Microwave Theory and Techniques, Vol. 49, No. 9, 1581-1592, Sep. 2001. doi:10.1109/22.942570
3. Appleby, R., D. A. Wikner, R. Trebits, and J. L. Kurtz, "Mechanically scanned real-time passive millimeter-wave imaging at 94 GHz," Proceedings of the IEEE, Vol. 5077, 1-6, 2003.
4. Chen, H.-M., S. Lee, R. M. Rao, M. A. Slamani, and P. K. Varshney, "Imaging for concealed weapon detection: A tutorial overview of development in imaging sensors and processing," IEEE Signal Processing Magazine, Vol. 22, No. 2, 52-61, Mar. 2005. doi:10.1109/MSP.2005.1406480
5. Fetterman, M. R., J. Grata, G. Jubic, W. L. Kiser, Jr., and A. Visnansky, "Simulation, acquisition and analysis of passive millimeter-wave images in remote sensing applications," Optics Express, Vol. 16, No. 25, 20503-20515, Dec. 2008. doi:10.1364/OE.16.020503
6. Camps, A., J. Bara, I. C. Sanahuja, and F. Torres, "The processing of hexagonally sampled signals with standard rectangular techniques: Application to 2-D large aperture synthesis interferometric radiometers," IEEE Trans. Geosci. & Remote Sens., Vol. 35, No. 1, 183-190, Jan. 1997. doi:10.1109/36.551946
7. Tanner, B. A., H. B. Lambrigsten, M. T. Gaier, and F. Torres, "Near field characterization of the GeoSTAR demonstrator," Proceedings of IEEE Geosci. Remote Sens. Symp., Denver, Co, USA, Jul. 2006.
8. Lucotte, B. M., B. Grafulla-Gonzalez, and R. A. Harvey, "Array rotation aperture synthesis for short range imaging at millimeter wavelengths," Radio Science, Vol. 44, No. 1, RS1006-1-RS1006-11, 2009. doi:10.1029/2008RS003863
9. Mait, J. N., D. R. Martin, A. C. Schuetz, and W. D. Prather, "Millimeter wave imaging with engineered point spread functions," Optical Engineering, Vol. 51, No. 9, 091606-1, May 2012. doi:10.1117/1.OE.51.9.091606
10. Rasche, V., R. Proksa, R. Sinkus, P. Bornert, and H. Eggers, "Resampling of data between arbitrary grids using convolution interpolation," IEEE Trans. Medical Imaging, Vol. 18, No. 5, 385-392, May 1999. doi:10.1109/42.774166
11. Fessler, J. A. and P. B. Sutton, "Nonuniform fast Fourier transforms using min-max interpolation," IEEE Trans. Signal Processing, Vol. 51, No. 2, 560-574, Feb. 2003. doi:10.1109/TSP.2002.807005
12. Beatty, P. J., G. D. Nishimura, and M. J. Pauly, "Rapid gridding reconstruction with a minimal oversampling ratio," IEEE Trans. Medical Imaging, Vol. 24, No. 6, 799-808, Jun. 2005. doi:10.1109/TMI.2005.848376
13. Lannes, A., E. Anterrieu, and K. Bouyouvcef, "Fourier interpolation and reconstruction vis Shannontype techniques; Part I: Regularization principle," J. Modern Opt., Vol. 41, No. 8, 1537-1574, 1994. doi:10.1080/09500349414552411
14. Lannes, A., E. Anterrieu, and K. Bouyouvcef, "Fourier interpolation and reconstruction vis Shannon type techniques; Part II: Technical developments and applications," J. Modern Opt., Vol. 43, No. 1, 105-138, 1996. doi:10.1080/09500349608232728
15. Picard, B. and E. Anterrieu, "Comparison of regularized inversion methods in synthetic aperture imaging radiometry," IEEE Trans. Geosci. & Remote Sens., Vol. 43, No. 2, 218-224, Feb. 2005. doi:10.1109/TGRS.2004.841482
16. Camps, A., J. Bar'a, F. Torres, and I. Corbella, "Extension of the CLEAN technique to the microwave imaging of continuous thermal sources by means of aperture synthesis radiometers," Progress In Electromagnetics Research, Vol. 18, 67-83, 1998. doi:10.2528/PIER97041500
17. Zhang, C., J. Wu, H. Liu, and Y. J. Yan, "Imaging algorithm for synthetic aperture interferometric radiometer in near field," Science China Technological Sciences, Vol. 54, No. 8, 2224-2231, Aug. 2011. doi:10.1007/s11431-011-4403-3
18. Yao, X., C. Zheng, J. Zhang, B. Yang, A. Hu, and J. Miao, "Near field image reconstruction algorithm for passive millimeter-wave imager bhu-2D-u," Progress In Electromagnetics Research C, Vol. 45, 57-72, Oct. 2013.
19. Chen, J., Y. Li, J. Wang, Y. Li, and Y. Zhang, "An accurate imaging algorithm for millimeter wave synthetic aperture imaging radiometer in near-field," Progress In Electromagnetics Research, Vol. 141, 517-535, Aug. 2013. doi:10.2528/PIER13060702
20. Fessler, J. A. and W. L. Rogers, "Spatial resolution properties of penalized-likelihood image reconstruction methods: Space-invariant tomographs," IEEE Trans. Imag. Process., Vol. 5, No. 9, 1346-1358, Sep. 1996. doi:10.1109/83.535846
21. Figueiredo, M. A. T., R. D. Nowak, and S. J.Wright, "Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems," IEEE Journal of Selected Topics n Signal Processing, Vol. 1, No. 4, 586-597, Apr. 2007. doi:10.1109/JSTSP.2007.910281
22. Hale, E. T., W. Yin, and Y. Zhang, "Fixed-point continuation for L1 minimization: Methodology and convergence," SIAM Journal on Optimization, Vol. 19, No. 3, 1107-1130, Oct. 2008. doi:10.1137/070698920
23. 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, Mar. 2009. doi:10.1137/080716542
24. Wright, S. J., R. D. Nowak, and M. A. T. Figueiredo, "Sparse reconstruction by separable approximation," IEEE Trans. Signal Processing, Vol. 57, No. 7, 2479-2493, Jul. 2009. doi:10.1109/TSP.2009.2016892