Article

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; 59(7):3251 - 3261. 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.

0 Followers
 · 
224 Views
  • Source
  • [Show abstract] [Hide abstract]
    ABSTRACT: We introduce a new approach using the Bayesian framework for the reconstruction of sparse Synthetic Aperture Radar (SAR) images. The algorithm, named SLIM, can be thought of as a sparse signal recovery algorithm with excellent sidelobe suppression and high resolution properties. For a given sparsity promoting prior, SLIM cyclically minimizes a regularized least square cost function. We show how SLIM can be used for SAR image reconstruction as well as SAR image enhancement. We evaluate the performance of SLIM by using realistically simulated complex-valued backscattered data from a backhoe vehicle. The numerical results show that SLIM can satisfactorily suppress the sidelobes and yield higher resolution than the conventional matched filter or delay-and-sum (DAS) approach. SLIM outperforms the widely used compressive sampling matching pursuit (CoSaMP) algorithm, which requires the delicate choice of user parameters. Compared with the recently developed iterative adaptive approach (IAA), which iteratively solves a weighted least squares problem, SLIM is much faster. Due to the computational complexity involved with SAR imaging, we show how SLIM can be made even more computationally efficient by utilizing the fast Fourier transform (FFT) and conjugate gradient (CG) method to carry out its computations. Furthermore, since SLIM is derived under the Bayesian model, the a posteriori distribution given by the algorithm provides us with a confident measure regarding the statistical properties of the SAR image pixels.
    Digital Signal Processing 05/2013; 23(3):852–858. DOI:10.1016/j.dsp.2012.10.009 · 1.50 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: This work contemplates advanced signal processing techniques for narrow band pulsed radar systems. If we assume a sparse scene of point-like targets and formulate the data model for the received signal in Fourier space, we can produce a block sparse estimation problem for the range profile spectra in all relevant Doppler channels. The range profile spectra are jointly estimated by coherent versions of block matching pursuit and basis pursuit algorithms. Then, in each Doppler channel, we compute the delays using a parametric high-resolution method. The mixed sparse/parametric approach overcomes the disadvantages of matched filters concerning resolution and ambiguities and has less computational complexity than full two-dimensional sparse estimation methods. We show results from numerical simulations and experimental measurements recorded with a passive bistatic radar using Global System for Mobil Communications (GSM) base stations as illuminators of opportunity.
    IEEE Transactions on Aerospace and Electronic Systems 04/2014; 50(2):843-857. DOI:10.1109/TAES.2013.120455 · 1.39 Impact Factor

Preview

Download
10 Downloads
Available from