An efficient algorithm for two-dimensional autoregressive spectrum estimation

McGuffin, B.F.; Liu, B.

doi:10.1109/29.17507

Cited by 26 publications

(6 citation statements)

References 17 publications

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“…Estimation of two-dimensional (2D) frequencies is a key problem in many areas such as wireless communications, joint frequency and wave-number estimation in array processing, synthetic aperture radar imaging, and nuclear magnetic resonance imaging [1][2][3][4][5][6][7][8][9][10][11][12]. For example, in the furnace temperature control system of silicon single crystal growth [13], the temperature measurement is affected by the Argon inflation, Crucible turn and rise, Crystal rotation and ascent, and so forth.…”

Section: Introductionmentioning

confidence: 99%

“…The maximumlikelihood (ML) method [3][4][5], despite its theoretical optimality, has extremely demanding computational complexity. Some high-resolution techniques, such as autoregressive method [6] and maximum entropy method [7], have limited applications due to spectral peak search in 2D plane. Kay and Nekovei proposed a computationally efficient algorithm in [8], but it is applied to only the single 2D sinusoid case.…”

Section: Introductionmentioning

confidence: 99%

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Two-Dimensional Frequencies Estimation Using Two-Stage Separated Virtual Steering Vector-Based Algorithm

Liu

Liang

2011

EURASIP J. Adv. Signal Process.

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In this paper, we develop a novel two-stage separated virtual steering vector-(SVSV-) based algorithm without association operation to estimate 2D frequencies. The key points of this algorithm are (i) in the first stage, this paper rearranges the measurement data as virtual rectangular array data matrix and obtains the propagator from the data matrix using least-squares operator. In addition, the virtual steering vector can be separated into two parts using the introduced electric angle that combines 2D frequencies (to avoid incorrect association especially when multiple 2D frequencies have the same frequency at some dimension), and thus the electric angle and the first part of separated steering vector can be estimated using the derived rank-reduction propagator method; (ii) in the second stage, this paper estimates the second part of separated steering vector using another least-squares operator and obtains 2D frequencies from the recovered steering vector. The resultant SVSV algorithm does not require spectral search or pairing parameters or singular value decomposition (SVD) of data matrix. Simulation results are presented to validate the performance of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two-Dimensional Frequencies Estimation Using Two-Stage Separated Virtual Steering Vector-Based Algorithm

Liu

Liang

2011

EURASIP J. Adv. Signal Process.

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“…The table groups the algorithms on the basis of their rationale. Many of these algorithms are discussed in [4]- [7], and in a vast spectral estimation and array processing literature, for example [8]- [32]. However, RRMVM [44], ASR [45], [46], and SVA [48], [49] are new, as is much of the literature describing the application of spectral estimation algorithms to radar cross-section (RCS) analysis and imaging [33]- [49].…”

Section: -D Spectral Estimation Algorithmsmentioning

confidence: 99%

“…While this truncation improves the apparent TCR, and improves the accuracy of point scattering peak locations in the imagery, it does not improve the image domain TCR. Thus, the TKARLP prediction filter is the minimum-norm solution to which is (32) where the eigendecomposition of the reduced correlation matrix is One obtains the corresponding error prediction filter by inserting a one in the th entry of the prediction filter and obtains the TKARLP image -…”

Section: ) Eigenvector and Multiple Signal Classificationmentioning

confidence: 99%

SAR imaging via modern 2-D spectral estimation methods

DeGraaf

1998

IEEE Trans. on Image Process.

219

116

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This paper discusses the use of modern 2D spectral estimation algorithms for synthetic aperture radar (SAR) imaging. The motivation for applying power spectrum estimation methods to SAR imaging is to improve resolution, remove sidelobe artifacts, and reduce speckle compared to what is possible with conventional Fourier transform SAR imaging techniques. This paper makes two principal contributions to the field of adaptive SAR imaging. First, it is a comprehensive comparison of 2D spectral estimation methods for SAR imaging. It provides a synopsis of the algorithms available, discusses their relative merits for SAR imaging, and illustrates their performance on simulated and collected SAR imagery. Some of the algorithms presented or their derivations are new, as are some of the insights into or analyses of the algorithms. Second, this work develops multichannel variants of four related algorithms, minimum variance method (MVM), reduced-rank MVM (RRMVM), adaptive sidelobe reduction (ASR) and space variant apodization (SVA) to estimate both reflectivity intensity and interferometric height from polarimetric displaced-aperture interferometric data. All of these interferometric variants are new. In the interferometric contest, adaptive spectral estimation can improve the height estimates through a combination of adaptive nulling and averaging. Examples illustrate that MVM, ASR, and SVA offer significant advantages over Fourier methods for estimating both scattering intensity and interferometric height, and allow empirical comparison of the accuracies of Fourier, MVM, ASR, and SVA interferometric height estimates.

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“…(4) leads to the following system of equations however possess a shift invarince property which b y the use of proper permutations results to a near to Toeplitz structure. As a result, efficient algorithms analogous to [7], can be developed.…”

Section: Fast Algorithms For Batch Ls Filteringmentioning

confidence: 99%

Fast algorithms for 2-D least squares FIR filtering

Glentis

Kaloupstidis

1991

[Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing

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Paiiepistimiopolis, TYPA Buildings, 157 71 ATHENS, GR.EECE. A B S T R A C T . This paper is concerned with the development of fast batch and adaptive algorithms for Two Dimensional (2-D) least squares (LS) FIR filtering. The proposed algorithms accommodate filter masks with arbitrary boundaries shape, and utilize scalar operations, only. 1. P r o b l e m forinulation We shall deal with the general 2-D FIR filter Such filters are used in a wide range of applications.Typical examples include digital restoration of coloured images, classification and segmentation, pattern recognition and object detection, and 2-D spectral estimation, [11-[51. Extension of the results to multidimensional signals can be carried out with analogous arguments. We shall allow for general support regions, (filter masks), R. Thus, R can be strongly causal, causal, semicausal and/or noncausal. More precisely, R consists of a union of intervals, C l e a r l y , P = m a x { k : ( k , l ) E R } , c r = m i n { k : ( k , l ) E R},Examples of causal and noncausal regions are illustrated in Fig. 1, (a-b). The engagement of varying length intervals Sl;, ~k , enables the incorporation of masks with very general boundaries, for instance, smooth curves like circles or parabolas, see Fig. 1, (c).Let z(m, 72) denote the desired response 2-D signal.We seek to determine the FIR structure that minimizes some function of the error, e(m,n) = z(m,n)y(m,vx). Two criteria will be considered. The mean squared error and the total squared error In the former case, both input and desired response 2-D signals are random fields, possessing certain stationarity properties that will be explained below. In the second case, samples of z ( m , n ) and s(nz,n) are assuiiied available on the observation region [ M I N I ] x [MzNz]. Efficient algorithms for batch and adaptive LS filtering can be derived if a shift invariance property prevails. The method of [6], uses extended filter masks, R, R E. R, that enables the formulation of fast adaptivestructures. This overparametrization approach, however, increases computational complexity and memory needs.In this paper, we introduce suitable permutations that unravel shift invariance properties and enable the development of fast batch and adaptive LS algorithms for 2-D FIR filters with general masks. Fast algorithms for batch LS filteringTo come up with a format amenable to efficient coinputation we manipulate eq. (1) as follows,-3009 -CH2977-719110000-3009 $1.00 0 1991 IEEE

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An efficient algorithm for two-dimensional autoregressive spectrum estimation

Cited by 26 publications

References 17 publications

Two-Dimensional Frequencies Estimation Using Two-Stage Separated Virtual Steering Vector-Based Algorithm

Two-Dimensional Frequencies Estimation Using Two-Stage Separated Virtual Steering Vector-Based Algorithm

SAR imaging via modern 2-D spectral estimation methods

Fast algorithms for 2-D least squares FIR filtering

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