Sparse Iterative Covariance Estimation-based Approach for Spectral Analysis and Reconstruction of Missing Data
MA Juntao①② GAO Meiguo① DONG Jian②
①(School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China) ②(Department of Electronic and Optical Engineering, Ordance Engineering College, Shijiazhuang 050003, China)
Many researches confirmed the excellent performance of Iterative Adaptive Approach (IAA), when it is applied to spectrum analysis of missing data. Simulation results show that the IAA can use 20 percent of the data to recover the missing samples, which is superior to Gapped Amplitude and Phase EStimation (GAPES). But the reconstruction performance of IAA degrades rapidly when the missing data exceed 80%. This paper introduces a novel method of missing data spectrum analysis, and a relevant modified method of time-domain reconstruction is proposed, called Missing SParse Iterative Covariance-based Estimation(M-SPICE). This method converts the weighted missing data covariance fitting cost function to a convex optimization problem. The global convergence property is obtained by adopting cyclic minimizers. The time-domain reconstruction method is modified by renewing estimation operator, which increases the accuracy of the data reconstruction in the case of underestimation. The simulation indicates that the novel method can be used to estimate the missing data spectrum, and reconstruct missing data accurately, with even fewer valid samples, regardless of gapped or arbitrary missing patterns.
STOICA P, LARSSON E G, and LI Jian. Adaptive filter-bank approach to restoration and spectral analysis of gapped data[J]. The Astronomical Journal, 2000, 120(4): 2163-2173.
[2]
SCHAFER J L and GRAHAM J W. Missing data: our view of the state of the art[J]. Psychological Methods, 2002, 7(2): 147-177.
[3]
BAI Xueru, ZHOU Feng, XING Mengdao, et al. High- resolution radar imaging of air targets from sparse azimuth data[J]. IEEE Transactions on Aerospace and Electronic Systems, 2012, 48(2): 1643-1655.
WANG Cheng, HU Weidong, and DU Xiaoyong, et al. The super-resolution range imaging based on sparse band multiple frequency bands radars signal fusion[J]. Acta Electronica Sinica, 2006, 34(6): 985-990.
LIU Qi, HONG Wen, TAN Weixian, et al. Adaptive tuning missing-data amplitude and phase estimation method in wide angle SAR[J]. Journal of Electronics & Information Technology, 2012, 34(3): 616-621. doi: 10.3724/SP.J.1146. 2011.00650.
TIAN Biao, LIU Yang, XU Shiyou, et al. Multi-band fusion imaging based on high precision parameter estimation of geometrical theory of diffraction model[J]. Journal of Electronics & Information Technology, 2013, 35(7): 1532-1539. doi: 10.3724/SP.J.1146.2012.01364.
[7]
YARDIBI T, LI Jian, STOICA P, et al. Source localization and sensing: a nonparametric iterative adaptive approach based on weighted least squares[J]. IEEE Transactions on Aerospace and Electronic Systems, 2010, 46(1): 425-443.
[8]
SUN W, SO H C, CHEN Y, et al. Approximate subspace- based iterative adaptive approach for fast two-dimensional spectral estimation[J]. IEEE Transactions on Signal Processing, 2014, 62(12): 3220-3231.
[9]
ZHANG Yongchao, ZHANG Yin, LI W, et al. Divide and conquer: a fast matrix inverse method of iterative adaptive approach for real beam superresolution[C]. International Geoscience and Remote Sensing Symposium (IGARSS), Québec City, 2014: 698-701.
[10]
GLENTIS G O, JAKOBSSON A, and ANGELOPOULOS K. Block-recursive IAA-based spectral estimates with missing samples using data interpolation[C]. International Conference on Acoustics, Speech and Signal Processing (ICASSP), Florence, 2014: 350-354.
[11]
STOICA P, LI Jian, and LING J. Missing data recovery via a nonparametric iterative adaptive approach[J]. IEEE Signal Processing Letters, 2009, 16(4): 241-244.
[12]
GLENTIS G O, ZHAO K, JAKOBSSON A, et al. Non-parametric high-resolution SAR imaging[J]. IEEE Transactions on Signal Processing, 2013, 61(7): 1614-1624.
[13]
KARLSSON J, ROWE W, XU L, et al. Fast missing-data IAA with application to notched spectrum SAR[J]. IEEE Transactions on Aerospace Electronic Systems, 2014, 50(2): 959-971.
[14]
STOICA P, PRABHU Babu, and LI Jian. New method of sparse parameter estimation in separable models and its use for spectral analysis of irregularly sampled data[J]. IEEE Transactions on Signal Processing, 2011, 59(1): 35-47.
[15]
STOICA P, PRABHU Babu, and LI Jian. SPICE: a sparse covariance-based estimation method for array processing [J]. IEEE Transactions on Signal Processing, 2011, 59(2): 629-638.
[16]
PARK H R and LI Jie. Sparse covariance-based high resolution time delay estimation for spread spectrum signals [J]. Electronics Letters, 2015, 51(2): 155-157.
