SCIENCE CHINA Information Sciences, Volume 60 , Issue 8 : 082302(2017) https://doi.org/10.1007/s11432-015-1016-x

Fast FOCUSS method based on bi-conjugate gradient and its application to space-time clutter spectrum estimation

Gatai BAI 1,3, Ran TAO 1,2,3,*, Juan ZHAO 2,3, Xia BAI 2,3, Yue WANG 1,2,3
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  • ReceivedOct 8, 2016
  • AcceptedDec 29, 2016
  • PublishedFeb 24, 2017




This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61421001, 61331021, 61671060).


[1] Gorodnitsky I F, George J S, Rao B D. Neuromagnetic source imaging with FOCUSS: a recursive weighted minimum norm algorithm. Electroencephalogr Clin Neurophysiol, 1995, 95: 231-251 CrossRef Google Scholar

[2] Gorodnitsky I F, Rao B D. Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm. IEEE Trans Signal Process, 1997, 45: 600-616 CrossRef Google Scholar

[3] Yang X Y, Chen B X, Chen Y H. An eigenstructure-based 2D DOA estimation method using dual-size spatial invariance array. Sci China Inf Sci, 2011, 54: 163-171 Google Scholar

[4] Sun K, Meng H, Wang Y, et al. Direct data domain STAP using sparse representation of clutter spectrum. Signal Process, 2011, 91: 2222-2236 CrossRef Google Scholar

[5] Alonso M T, Lopez-Dekker P, Mallorqui J J. A novel strategy for radar imaging based on compressive sensing. IEEE Trans Geosci Remote Sens, 2010, 48: 4285-4295 CrossRef Google Scholar

[6] Bu H X, Bai X, Tao R. Compressed sensing SAR imaging based on sparse representation in fractional Fourier domain. Sci China Inf Sci, 2012, 55: 1789-1800 CrossRef Google Scholar

[7] Yang J Y, Peng Y G, Xu W L, et al. Ways to sparse representation: an overview. Sci China Ser F-Inf Sci, 2009, 52: 695-703 CrossRef Google Scholar

[8] Tropp J. Greed is good: algorithmic results for sparse approximation. IEEE Trans Inf Theory, 2004, 50: 2231-2242 CrossRef Google Scholar

[9] Wu R, Huang W, Chen D R. The exact support recovery of sparse signals with noise via orthogonal matching pursuit. IEEE Signal Process Lett, 2013, 20: 403-406 CrossRef Google Scholar

[10] Chen S S, Donoho D L, Saunders M A. Atomic decomposition by basis pursuit. SIAM J Sci Comput, 1998, 20: 33-161 CrossRef Google Scholar

[11] Selesnick I W, Bayram I. Sparse signal estimation by maximally sparse convex optimization. IEEE Trans Signal Process, 2014, 62: 1078-1092 CrossRef Google Scholar

[12] Rao B D, Kreutz-Delgado K. An affine scaling methodology for best basis selection. IEEE Trans Signal Process, 1999, 47: 187-200 CrossRef Google Scholar

[13] Xie K, He Z, Cichocki A. Convergence analysis of the FOCUSS algorithm. IEEE Trans Neural Netw Learn Syst, 2015, 26: 601-613 CrossRef Google Scholar

[14] He Z, Cichocki A, Zdunek R, et al. Improved FOCUSS method with conjugate gradient iteration. IEEE Trans Signal Process, 2009, 57: 399-404 CrossRef Google Scholar

[15] Hu C X, Liu Y M, Li G, et al. Improved FOCUSS method for reconstruction of cluster structured sparse signals in radar imaging. Sci China Inf Sci, 2012, 55: 1776-1788 CrossRef Google Scholar

[16] Sun K, Zhang H, Li G, et al. Airborne radar STAP using sparse recovery of clutter spectrum. arXiv:1008.4185. Google Scholar

[17] Yang Z, de Lamare R C, Li X. Sparsity-aware space-time adaptive processing algorithms with L1-norm regularization for airborne radar. IET Signal Process, 2012, 6: 413-423 CrossRef Google Scholar

[18] Yang Z, Li X, Wang H, et al. On clutter sparsity analysis in space-time adaptive processing airborne radar. IEEE Geosci Remote Sens Lett, 2013, 10: 1214-1218 CrossRef Google Scholar

[19] Wang L, Liu Y, Ma Z, et al. A novel STAP method based on structured sparse recovery of clutter spectrum. In: Proceedings of IEEE Radar Conference (RadarCon), Arlington, 2015. 561--565. Google Scholar

[20] Yang Z, Liu Z, Li X, et al. Performance analysis of STAP algorithms based on fast sparse recovery techniques. Prog Electromagn Res B, 2012, 41: 251-268 CrossRef Google Scholar

[21] Sen S. Low-rank matrix decomposition and spatio-temporal sparse recovery for STAP radar. IEEE J Sel Top Signal Process, 2015, 9: 1510-1523 CrossRef Google Scholar

[22] Fletcher R. Conjugate gradient methods for indefinite systems. In: Numerical Analysis. Berlin: Springer, 1976. 73--89. Google Scholar

[23] Joly P, Meurant G. Complex conjugate gradient methods. Numer Math, 1993, 4: 379-406 Google Scholar

[24] Mihalyffy L. An alternative representation of the generalized inverse of partitioned matrices. Linear Algebra Appl, 1971, 4: 95-100 CrossRef Google Scholar

[25] Saad Y. Iterative Methods for Sparse Linear Systems. Boston: PWS-Kent, 1995. Google Scholar

[26] Bank R E, Chan T F. An analysis of the composite step biconjugate gradient algorithm for solving nonsymmetric systems. Numer Math, 1993, 66: 295-319 CrossRef Google Scholar

[27] Rao B D, Engan K, Cotter S F, et al. Subset selection in noise based on diversity measure minimization. IEEE Trans Signal Process, 2003, 51: 760-770 CrossRef Google Scholar

[28] Peng Y, Fei Y, Feng Y. Sparse array synthesis with regularized FOCUSS algorithm. In: Prceedings of International Symposium of the IEEE Antennas and Propagation Society, 2013. 1406--1407. Google Scholar

[29] Golub G H, Van-Loan C F. Matrix Computations. 3rd ed. Boltimore and London: The Johns Hopkins University Press, 1996. Google Scholar

[30] Duan K Q, Xie W C, Wang Y L. Nonstationary clutter suppression for airborne conformal array radar. Sci China Inf Sci, 2011, 54: 2170-2177 CrossRef Google Scholar

[31] Wu R B, Jia Q Q, Li H. A novel STAP method for the detection of fast air moving targets from high speed platform. Sci China Inf Sci, 2012, 55: 1259-1269 CrossRef Google Scholar

[32] Peckham C D, Haimovich A M, Ayoub T F, et al. Reduced-rank STAP performance analysis. IEEE Trans Aerosp Electron Syst, 2000, 36: 664-676 CrossRef Google Scholar


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