Abstract
In this paper, we present a description of a nonparametric two dimensional (2-D) procedure to extrapolate a signal, an extension of the Adaptive Weighted Norm Extrapolation (AWNE) method, and illustrate its application to SAR image formation. The benefits of the AWNE procedure are shown for synthetic data and for MSTAR data. Once the phase history is recovered, the AWNE method is applied to a subaperture or to the full set of frequency samples to extrapolate them to a larger aperture from which a superresolved complex SAR image is obtained. Use of the 2-D AWNE procedure proves to be superior to its one-dimensional separable version by reducing undesirable effects such as sidelobe interference, and variability in energy of the extrapolated data from row to row and column to column. To assess the performance of AWNE in enhancing prominent scatterers, reducing speckle, and suppressing clutter, we compare the superresolved images to the images formed with the traditional Fourier technique starting from the same phase history data. Fourier images are also compared with superresolved images formed using less data in order to assess the quality of the extrapolation and to quantify the method's ability to recover lost resolution. We illustrate performance by visual comparison and by the use of a geometric constellation of prominent point scatterers of the targets extracted from the images. A brief comparison with the 2-D versions of Capon and the linear prediction methods is illustrated and a hybrid AWNE/Capon approach is proposed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S.R. DeGraaf, “SAR Imaging via Modern 2-D Spectral Estimation Methods,” IEEE Trans. Image Process., vol. 7, May 1998, pp. 729–761.
L.M. Novak, G.R. Benitz, G.J. Owirka, and L.A. Bessette, “ATR Performance Using Enhanced Resolution SAR,” in SPIE, vol. 2757, Orlando, FL, April 1996, pp. 332–337.
J. Li and P. Stoica, “An Adaptive Filtering Approach to Spectral Estimation and SAR Imaging,” IEEE Trans. Signal Process., vol. 44, June 1996, pp. 1469–1484.
Z. Bi, J. Li, and Z.S. Liu, “Super Resolution SAR Image Formation via Parametric Spectral Estimation Methods,” in SPIE, vol. 3370, Orlando, FL, April 1998, pp. 238–249.
J. Li, P. Stoica, Z. Bi, R. Wu, and E.G. Zelnio, “A Robust Hybrid Spectral Estimation Algorithm for SAR Imaging,” in 32nd Asilomar Conf. on Signal, Systems and Computer, vol. 1, Pacific Grove, CA, October 1998, pp. 1322–1326.
F.M. Candocia and J.C. Principe, “A Method Using Multiple Models to Superresolve SAR Imagery,” in SPIE, vol. 3370, Orlando, FL, April 1998, pp. 197–207.
A.E. Brito, S.H. Chan, and S.D. Cabrera, “Application of AWNE Superresolution to MSTAR SAR Images,” in Proc. of IASTED SIP'98, vol. 1, Las Vegas, NV, May 1998, pp. 495–499.
A.E. Brito, S.H. Chan, and S.D. Cabrera, “SAR Image Formation Using 2-D Re-Weighted Minimum Norm Extrapolation,” in SPIE Algorithm for SAR Radar Imagery VI, vol. 3721, Orlando, FL, April 1999, pp. 78–91.
S.D. Cabrera and T.W. Parks, “Extrapolation and Spectral Estimation with Iterative Weighted Norm Modification,” IEEE Trans. Signal Process., vol. 39, April 1991, pp. 842–851.
M.D. Sacchi, T.J. Ulrych, and C.J. Walker, “Interpolation and Extrapolation Using a High-Resolution Discrete Fourier Transform,” IEEE Trans. Signal Process., vol. 46, January 1998, pp. 31–38.
A.E. Brito, “Iterative Adaptive Extrapolation Applied to SAR Image Formation and Sinusoidal Recovery,” PhD thesis, Department of Electrical and Computer Engineering, The University of Texas at El Paso, El Paso, TX, 2001.
“Sensor Data Management System Page,” http: //www.mbvlab.wpafb.af.mil/public/MBVDATA.
A.K. Jain and S. Ranganath, “Extrapolation Algorithms for Discrete Signals with Application in Spectral Estimation,” IEEE Trans. Acoust. Speech Signal Process, vol. ASSP-29, September 1981, pp. 830–845.
A. Papoulis, “A New Algorithm in Spectral Analysis and Band-Limited Extrapolation,” IEEE Trans. Circuits Syst., vol. CAS-22, September 1975, pp. 735–742.
C.L. Byrne and R.M. Fitzgerald, “Reconstruction from Partial Information with Applications to Tomography,” SIAM Journal on Applied Mathematics, vol. 42, August 1982, pp. 933–940.
C.L. Byrne and R.M. Fitzgerald, “Spectral Estimators that Extend the Maximum Entropy and Maximum Likelihood Method,” SIAM Journal on Applied Mathematics, vol. 44, April 1984, pp. 425–442.
L. Potter and K. Arun, “Energy Concentration in Band-Limited Extrapolation,” IEEE Trans. Acoust. Speech Signal Process., vol. 37, July 1989, pp. 1027–1041.
E. Diethorn and J. Munson, D.C., “A Linear, Time-Varying System Framework for Noniterative Discrete-Time Band-Limited Signal Extrapolation,” IEEE Trans. Signal Process., vol. 39, January 1991, pp. 55–68.
S. Dharanipragada and K. Arun, “Bandlimited Extrapolation Using Time-Bandwidth Dimension,” IEEE Trans. Signal Process, vol. 45, December 1997, pp. 2951–2966.
S.H. Chan, A.E. Brito, and S.D. Cabrera, “Characterization of Windowing Effects in Adaptive Extrapolation of Sinusoids,” in 33rd Asilomar Conf. on Signals, Systems and Computers, vol. 2, Pacific Grove, CA, October 1999, pp. 1092–1097.
S.H. Chan, A.E. Brito, and S.D. Cabrera, “Imposed Window Estimate for Adaptive Extrapolation of Complex Sinusoids in Gaussian Noise,” in 9th IEEE DSP Workshop, Hunt, TX, October 2000.
A.E. Brito and S.D. Cabrera, “Analysis of Autocorrelation Pursuit via Non-Parametric Iterative Extrapolation,” in 35th Annual Conference on Information Sciences and Systems, vol. 2, Baltimore, MD: Johns Hopkins University, March 2001, pp. 633–638.
J.S. Lim, Two-Dimensional Signal and Image Processing, Englewood Cliffs, New Jersey: Prentice-Hall, 1990.
B.L. Burns and J.T. Cordaro, “A SAR Image-Formation Algorithm that Compensates for the Spatially-Variant Effects of Antenna Motion,” in SPIE, vol. 2230, Orlando, FL, April 1994, pp. 14–24.
W.W. Irving, R.B. Washburn, and W.E.L. Grimson, “Bounding Performance of Peak-Based Target Detectors,” in SPIE, vol. 3070, Orlando, FL, April 1997, pp. 245–257.
B. Bhanu and G. Jones III, “Performance Characterization of a Model-Based SAR Target Recognition System Using Invariants,” in SPIE, vol. 3070, Orlando, FL, April 1997, pp. 305–321.
S.M. Kay, Modern Spectral Estimation, Englewood Cliffs, NJ: Prentice Hall, 1988.
S.L. Marple, Digital Spectral Analysis with Applications, Englewood Cliffs, NJ: Prentice Hall, 1987.
A. Jakobsson, S.L. Marple, and P. Stoica, “Computationally Efficient Two-Dimensional Capon Spectrum Analysis,” IEEE Trans. Signal Process., vol. 48, September 2000, pp. 2651–2661.
E.G. Larsson and P. Stoica, “Fast Implementation of Two-Dimensional APES and Capon Spectral Estimators,” in Proc. IEEE ICASSP, vol. V, Salt Lake City, UT, March 2001, pp. 3069–3072.
Rights and permissions
About this article
Cite this article
Brito, A.E., Chan, S.H. & Cabrera, S.D. SAR Image Superresolution via 2-D Adaptive Extrapolation. Multidimensional Systems and Signal Processing 14, 83–104 (2003). https://doi.org/10.1023/A:1022221024995
Issue Date:
DOI: https://doi.org/10.1023/A:1022221024995