Efficient Super-Resolution Two-Dimensional Harmonic Retrieval Via Enhanced Low-Rank Structured Covariance Reconstruction

Wang, Yue; Tian, Zhi; Leus, Geert; Zhang, Gong

doi:10.1109/icassp40776.2020.9054756

Cited by 6 publications

(6 citation statements)

References 22 publications

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“…The noise tolerance constraint in (34c) has to be imposed in RR-D-ANM-R, which can be rewritten equivalently as (c.f. our recent work in [49]):…”

Section: Efficient Relaxationmentioning

confidence: 95%

“…where the user-specified parameter η p can be uniquely determined from ( 48) by the degrees of freedom M 2 and a prefixed allowable deviation probability p 1, independent of noise variance σ 2 0 . Adopting (49) as an alternative error tolerance constraint to replace (33c) and (34c), and replacing R y in (49) by vec −1 (Γvec(Z) + (J * ⊗ J )vec(diag(σ 2 0 ))), the proposed RR-D-ANM and RR-D-ANM-R can be implemented without knowing the noise statistics. In fact, this alternative formulation allows to estimate the noise variance as a byproduct, at the cost of introducing another unknown variable σ 2 0 into (33) and (34).…”

Section: A Alternative Error Tolerance Constraint For Sufficient MMVmentioning

confidence: 99%

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Efficient Super-Resolution Two-Dimensional Harmonic Retrieval With Multiple Measurement Vectors

Wang

Tian

Leus

et al. 2022

IEEE Trans. Signal Process.

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This paper develops an efficient solution for superresolution two-dimensional (2D) harmonic retrieval from multiple measurement vectors (MMV). Given the sample covariance matrix constructed from the MMV, a gridless compressed sensing approach is proposed based on the atomic norm minimization (ANM). In the approach, our key step is to perform a redundancy reduction (RR) transformation that effectively reduces the large problem size at hand, without loss of useful frequency information. For uncorrelated sources, the transformed 2D covariance matrices in the RR domain retain a salient structure, which permits a sparse representation over a matrix-form atom set with decoupled 1D frequency components. Accordingly, the decoupled ANM (D-ANM) framework can be applied for superresolution 2D frequency estimation. Moreover, the resulting RRenabled D-ANM technique, termed RR-D-ANM, further allows an efficient relaxation under certain conditions, which leads to low computational complexity of the same order as the 1D case. Simulation results verify the advantages of our solutions over benchmark methods, in terms of higher computational efficiency and detectability for 2D harmonic retrieval.

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“…The noise tolerance constraint in (34c) has to be imposed in RR-D-ANM-R, which can be rewritten equivalently as (c.f. our recent work in [49]):…”

Section: Efficient Relaxationmentioning

confidence: 95%

Section: A Alternative Error Tolerance Constraint For Sufficient MMVmentioning

confidence: 99%

Efficient Super-Resolution Two-Dimensional Harmonic Retrieval With Multiple Measurement Vectors

Wang

Tian

Leus

et al. 2022

IEEE Trans. Signal Process.

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“…Accordingly, Ra is not only a low-rank matrix with rank K, but also holds an underlying Toeplitz-Hankel structure. Expanding the LRSCR theory [11][12][13][14], the augmented covariance Ra in (12) can be recovered by…”

Section: Low-rank Toeplitz-hankel Covariance Reconstructionmentioning

confidence: 99%

Super-Resolution Harmonic Retrieval of Non-Circular Signals

Wang¹,

Tian²,

Leus³

et al. 2023

Preprint

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This paper proposes a super-resolution harmonic retrieval method for uncorrelated strictly non-circular signals, whose covariance and pseudo-covariance present Toeplitz and Hankel structures, respectively. Accordingly, the augmented covariance matrix constructed by the covariance and pseudo-covariance matrices is not only low rank but also jointly Toeplitz-Hankel structured. To efficiently exploit such a desired structure for high estimation accuracy, we develop a low-rank Toeplitz-Hankel covariance reconstruction (LRTHCR) solution employed over the augmented covariance matrix. Further, we design a fitting error constraint to flexibly implement the LRTHCR algorithm without knowing the noise statistics. In addition, performance analysis is provided for the proposed LRTHCR in practical settings. Simulation results reveal that the LRTHCR outperforms the benchmark methods in terms of lower estimation errors.

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“…Remark 4: If we consider a multiple measurement vector (MMV) form of the virtual signal [29], the covariance-based formulation and similar DANM methods [36] can also be developed. To further reduce the computational complexity, the methodology of compressed sensing can be combined with DANM [37].…”

Section: B Atomic Norm Of Coarray Signal Matrixmentioning

confidence: 99%

“…In the second set of simulations, statistical results in terms of the RMSE are used to compare the estimation accuracy of CMT-BCS, SST, DANM and CRM. The covariance-based DANM methods, normal DANM (NDANM) [36], and low rank structured covariance reconstruction DANM (LRSCR-DANM) [37] are also included for comparison. The RMSE of a certain parameter ξ is defined as…”

Section: B Coarray Crb and Rmsementioning

confidence: 99%

Joint DoA-Range Estimation Using Space-Frequency Virtual Difference Coarray

Mao,

Liu,

Zhang

et al. 2022

Preprint

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In this paper, we address the problem of joint direction-of-arrival (DoA) and range estimation using frequency diverse coprime array (FDCA). By incorporating the coprime array structure and coprime frequency offsets, a two-dimensional space-frequency virtual difference coarray corresponding to uniform array and uniform frequency offset is considered to increase the number of degrees-of-freedom (DoFs). However, the reconstruction of the doubly-Toeplitz covariance matrix is computationally prohibitive. To solve this problem, we propose an interpolation algorithm based on decoupled atomic norm minimization (DANM), which converts the coarray signal to a simple matrix form. On this basis, a relaxation-based optimization problem is formulated to achieve joint DoA-range estimation with enhanced DoFs. The reconstructed coarray signal enables application of existing subspace-based spectral estimation methods. The proposed DANM problem is further reformulated as an equivalent rank-minimization problem which is solved by cyclic rank minimization. This approach avoids the approximation errors introduced in nuclear norm-based approach, thereby achieving superior root-mean-square error which is closer to the Cramér-Rao bound. The effectiveness of the proposed method is confirmed by theoretical analyses and numerical simulations.

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Efficient Super-Resolution Two-Dimensional Harmonic Retrieval Via Enhanced Low-Rank Structured Covariance Reconstruction

Cited by 6 publications

References 22 publications

Efficient Super-Resolution Two-Dimensional Harmonic Retrieval With Multiple Measurement Vectors

Efficient Super-Resolution Two-Dimensional Harmonic Retrieval With Multiple Measurement Vectors

Super-Resolution Harmonic Retrieval of Non-Circular Signals

Joint DoA-Range Estimation Using Space-Frequency Virtual Difference Coarray

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