On Gridless Sparse Methods for Line Spectral Estimation From Complete and Incomplete Data

Yang, Zai; Xie, Lihua

doi:10.1109/tsp.2015.2420541

Cited by 271 publications

(184 citation statements)

References 54 publications

(125 reference statements)

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“…That is, the true signal DOAs may not necessarily fall on the exact discrete grid which is defined over a finite number of spatial angles. Off-grid sources cause so-called dictionary mismatch problem which violates the sparsity conditions and compromises the performance as well as the identifiability of the CS-based methods [19,20,21,22,23]. One solution to this problem is to use a denser search grid with an increased number of angles, thus leading to higher computational complexity.…”

Section: Introductionmentioning

confidence: 99%

Underdetermined wideband DOA estimation of off-grid sources employing the difference co-array concept

et al. 2017

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A wideband off-grid model is proposed to represent dictionary mismatch under the compressive sensing framework exploiting difference co-arrays. A group sparsity based off-grid method is proposed for underdetermined wideband direction of arrival (DOA) estimation which provides improved performance over the existing group sparsity based method with a same search grid. A two-step approach is then proposed which achieves an even better performance with significantly reduced computational complexity.

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Section: Introductionmentioning

confidence: 99%

Underdetermined wideband DOA estimation of off-grid sources employing the difference co-array concept

et al. 2017

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“…From a solution (X 11 , X 12 , X 22 ) of (4), we have r = rank(X 11 ) and the frequencies of the atoms a k = (1/ √ n)z n (ω k ) may be extracted by various methods, see e.g. [9,11,14].…”

Section: Sparse Optimizationmentioning

confidence: 99%

Multi-pitch estimation using semidefinite programming

Jensen

Vandenberghe

2017

2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Multi-pitch estimation concerns the problem of estimating the fundamental frequencies (pitches) and amplitudes/phases of multiple superimposed harmonic signals with application in music, speech, vibration analysis, and other fields. In this paper we formulate a complex-valued multi-pitch estimator via a semidefinite programming method for continuous sparse optimization over an infinite dictionary of vectors of complex exponentials and extend this to real-valued data via a real semidefinite program with the same dimensions (i.e. half the size). We further impose a continuous frequency constraint naturally occurring from assuming a Nyquist sampled signal by adding an additional semidefinite constraint. In our numerical experiments, the proposed estimator shows superior performance compared to state-of-the-art methods for separating two closely spaced fundamentals and approximately achieves the asymptotic Cramér-Rao lower bound.

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“…We know that the atomic set of ANM/RANM takes a continuous frequency value and can be regarded as a continuous dictionary that is the limiting scenario of the discretized dictionary in the GB-SR methods [10]. Without a discretized scheme, ANM/RANM can avoid the off-grid effect.…”

Section: A Anmmentioning

confidence: 99%

“…The GLS [10] method, which is a sparse and parametric method adopting the same covariance fitting criterion as SPICE [11] but without a discretizing scheme, is free of the off-grid effect and user parameters. According to (2), we suppose that the source signals and noise are uncorrelated.…”

Section: B Glsmentioning

confidence: 99%

“…Among them, the atomic norm minimization (ANM) [8], [9] and gridless sparse iterative covariance-based estimation (SPICE) (GLS) method [10] have shown outstanding performance in line spectral estimation and direction of arrival (DOA) estimation problems. However, to estimate the regularization parameter, ANM needs the noise variance a priori, which is difficult to exactly estimate from the incomplete observation.…”

mentioning

confidence: 99%

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DLSLA 3-D SAR Imaging Based on Reweighted Gridless Sparse Recovery Method

Bao

Peng²,

Wang

et al. 2016

IEEE Geosci. Remote Sensing Lett.

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Downward-looking sparse-linear-array 3-D synthetic aperture radar (DLSLA 3-D SAR) cross-track reconstruction usually suffers from incomplete observation and limited resolution. The incomplete observation is caused by the sparse and nonuniform distribution of the equivalent antenna phase centers (APCs) due to the array elements' installation location restriction, loss, or deviation. Sparse recovery methods provide a solution with improved resolution from the incomplete observation for the 3-D imaging scene that behaves with spatial sparsity. However, conventional grid-based sparse recovery (GB-SR) methods are under the assumption that the scatterers are located on the discretized grids; otherwise, the off-grid effect or basis mismatch problem will occur. In this letter, we propose a reweighted scheme-based gridless sparse recovery (GL-SR) method, i.e., reweighted gridless sparse iterative covariance-based estimation (RGLS), for DLSLA 3-D SAR cross-track imaging. The proposed method possesses the merits of gridless SPICE (GLS), i.e., free of off-grid effect and user parameters, and has a statistically more appealing property than GLS by adopting the reweighted scheme. As seen from the experiments that compare the performance of GB-SR and GL-SR methods for DLSLA 3-D SAR cross-track reconstruction, the proposed method performs outstandingly under the circumstance of sparse and nonuniform APCs' distribution.Index Terms-Downward-looking sparse-linear-array 3-D synthetic aperture radar (DLSLA 3-D SAR), gridless sparse recovery (GL-SR) method, reweighted scheme, sparse iterative covariancebased estimation (SPICE).

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On Gridless Sparse Methods for Line Spectral Estimation From Complete and Incomplete Data

Cited by 271 publications

References 54 publications

Underdetermined wideband DOA estimation of off-grid sources employing the difference co-array concept

Underdetermined wideband DOA estimation of off-grid sources employing the difference co-array concept

Multi-pitch estimation using semidefinite programming

DLSLA 3-D SAR Imaging Based on Reweighted Gridless Sparse Recovery Method

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