IAA Spectral Estimation: Fast Implementation Using the Gohberg–Semencul Factorization

Dept. of Electr. & Comput. Eng., Univ. of Florida, Gainesville, FL, USA
IEEE Transactions on Signal Processing (Impact Factor: 3.2). 08/2011; DOI: 10.1109/TSP.2011.2131136
Source: DBLP

ABSTRACT We consider fast implementations of the weighted least-squares based iterative adaptive approach (IAA) for one-dimensional (1-D) and two-dimensional (2-D) spectral estimation of uniformly sampled data. IAA is a robust, user parameter-free and nonparametric adaptive algorithm that can work with a single data sequence or snapshot. Compared to the conventional periodogram, IAA can be used to significantly increase the resolution and suppress the sidelobe levels. However, due to its high computational complexity, IAA can only be used in applications involving small-sized data. We present herein novel fast implementations of IAA using the Gohberg-Semencul (G-S)-type factorization of the IAA covariance matrices. By exploiting the Toeplitz structure of the said matrices, we are able to reduce the computational cost by at least two orders of magnitudes even for moderate data sizes.

  • [Show abstract] [Hide abstract]
    ABSTRACT: A synthetic aperture radar system operating in congested frequency bands suffers from radio frequency inter­ ference (RFI) from narrowband sources. When RFI interference is suppressed by frequency notching, gaps are introduced into the fast time phase history. This results in a missing data spectral estimation problem, where the missing data increases sidelobe energy and degrades image quality. The adaptive spectral estimation method Iterative Adaptive Approach (IAA) has been shown to provide higher resolution and lower sidelobes than comparable methods, but at the cost of higher computationally complexity. Current fast IAA algorithms reduce the computational complexity using Toeplitz /Vandermonde structures, but are not applicable for missing data cases because these structures are lost. When the number of missing data samples is small, which often is the case in SAR with RFI, we use a low rank completion to restore the Toeplitz/ Vandermonde structures. We show that the computational complexity of the proposed algorithm is considerably lower than the state-of-the-art and demonstrate the utility on a simulated frequency notched SAR imaging problem.
    SPIE Defense, Security, and Sensing; 06/2013
  • [Show abstract] [Hide abstract]
    ABSTRACT: High-resolution sparse spectral estimation techniques have recently been shown to offer significant performance gains as compared to most conventional estimation approaches, although such methods typically suffer the drawback of being computationally cumbersome. In this paper, we seek to alleviate this drawback somewhat, examining computationally efficient implementations of the recent iterative sparse maximum likelihood-based approaches (SMLA), exploiting the inherent rich structure of these estimators. The derived implementations reduce the resulting computational complexity with at least one order of magnitude, while still yielding exact implementations. The effectiveness of the discussed techniques are illustrated using experimental examples.
    2013 Asilomar Conference on Signals, Systems and Computers; 11/2013
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper focuses on suppressing spectral overlap for sub-band spectral estimation, with which we can greatly decrease the computational complexity of existing spectral estimation algorithms, such as nonlinear least squares spectral analysis and non-quadratic regularized sparse representation. Firstly, our study shows that the nominal ability of the high-order analysis filter to suppress spectral overlap is greatly weakened when filtering a finite-length sequence, because many meaningless zeros are used as samples in convolution operations. Next, an extrapolation-based filtering strategy is proposed to produce a series of estimates as the substitutions of the zeros and to recover the suppression ability. Meanwhile, a steady-state Kalman predictor is applied to perform a linearly-optimal extrapolation. Finally, several typical methods for spectral analysis are applied to demonstrate the effectiveness of the proposed strategy.
    Sensors (Basel, Switzerland). 01/2014; 15(1):110-34.


Available from