Frequency Estimation of Irregularly Sampled Data Using a Sparsity Constrained Weighted Least-Squares Approach

A. Zahedi, M. H. Kahaei


In this paper, a new method for frequency estimation of irregularly sampled data is proposed. In comparison with the previous sparsity-based methods where the sparsity constraint is applied to a least-squares fitting problem, the proposed method is based on a sparsity constrained weighted least-squares problem. The resulting problem is solved in an iterative manner, allowing the usage of the solution obtained at each iteration to determine the weights of the least-squares fitting term at the next iteration. Such an appropriate weighting of the least-squares fitting term enhances the performance of the proposed method. Simulation results verify that the proposed method can detect the spectral peaks using a very short data record. Compared to the previous one, the proposed method is less probable to miss the actual spectral peaks and exhibit spurious peaks.


basis pursuit; sparse representation; overcomplete dictionaries; irregular sampling; spectrum estimation

Full Text:



R. Pribic, “Radar irregular sampling”, IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '04, Vol. 3, pp. 933–936, 2004

S. Bourguignon, H. Carfantan, T. Böhm, “SparSpec: a new method for fitting multiple sinusoids with irregularly sampled data”, Astronomy and Astrophysics, Vol. 462, pp. 379–387, 2007

J. Mateo, P. Laguna, “Improved heart rate variability signal analysis from the beat occurrence times according to the IPFM model”, IEEE Transactions on Biomedical Engineering, Vol. 47, No. 8, pp. 985–996, 2000

L. H. Benedict, H. Nobach, C. Tropea, “Estimation of turbulent velocity spectra from laser Doppler data”, Measurement Science and Technology, Vol. 11, No. 8, pp. 1089–1104, 2000

N. R. Lomb, “Least-squares frequency analysis of unequally spaced data”, Astrophysics and Space Science, Vol. 39, No. 1, pp. 447–462, 1976

I. F. Gorodnitsky, B. D. Rao, “Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm”, IEEE Transactions on Signal Processing, Vol. 45, No. 3, pp. 600–616, 1997

M. D. Sacchi, T. J. Ulrych, C. J. Walker, “Interpolation and extrapolation using a high-resolution discrete Fourier transform”, IEEE Transactions on Signal Processing, Vol. 46, No. 1, pp. 31–38, 1998

P. Ciuciu, J. Idier J. –F. Giovannelli, “Regularized estimation of mixed spectra using a circular Gibbs-Markov model”, IEEE Transactions on Signal Processing, Vol. 49, No. 10, pp. 2202–2213, 2001

S. Chen, D. Donoho “Application of basis pursuit in spectrum estimation”, IEEE International Conference on Acoustics, Speech and Signal Processing, Vol. 3, pp. 1865–1868, 1998

S. Bourguignon, H. Carfantan, J. Idier, “A sparsity-based method for the estimation of spectral lines from irregularly sampled data”, IEEE Journal of Selected Topics in Signal Processing, Vol. 1, No. 4, pp. 575–585, 2007

S. S. Chen, D. L. Donoho, M. Saunders, “Atomic decomposition by basis pursuit”, SIAM Journal on Scientific Computing, Vol. 20, No. 1, pp. 33–61, 1999

D. L. Donoho, M. Elad, V. N. Temlyakov, “Stable recovery of sparse overcomplete representations in the presence of noise”, IEEE Transactions on Information Theory, Vol. 52, No. 1, pp. 6–18, 2006

P. Stoica, Jian Li, H. He, “Spectral analysis of nonuniformly sampled data: a new approach versus the periodogram”, IEEE Transactions on Signal Processing, Vol. 57, No. 3, pp. 843–858, 2009

W. Roberts, P. Stoica, Jian Li, T. Yardibi, F. A. Sadjadi, “Iterative adaptive approaches to MIMO radar imaging”, IEEE Journal of Selected Topics in Signal Processing: Special Issue on MIMO Radar and Its Applications, Vol. 4, No. 1, pp. 5–20, 2010

T. Yardibi, Jian Li, P. Stoica, Ming Xue, A. B. Baggeroer, “Source localization and sensing: a nonparametric iterative adaptive approach based on weighted least squares”, IEEE Transactions on Aerospace and Electronic Systems, Vol. 46, No. 1, pp. 425–443, 2010

D. Watkins, Fundamentals of matrix comutations, John Wiley and Sons, 2002

eISSN: 1792-8036     pISSN: 2241-4487