Low-Complexity Gridless 2D Harmonic Retrieval via Decoupled-ANM Covariance Reconstruction

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

doi:10.23919/eusipco47968.2020.9287680

Cited by 4 publications

(3 citation statements)

References 26 publications

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“…To take advantage of the low complexity of the D-ANM for the SMV case, we turn to r x = vec(R x ) ∈ C (N M ) 2 as the structured signal vector of interest. This vector can be approximated by vec 1 L X L X H L , which retains the useful 2D frequency information in all the columns of X L . Hence, an MMV problem based on X L can be alternatively solved as an SMV problem based on r x , which is amenable to the D-ANM.…”

Section: A Redundancy-reduction Transformationmentioning

confidence: 99%

“…Considering the computational efficiency of D-ANM over V-ANM, we aim to develop a D-ANM solution to extract the structural information of the RR vector z. To this end, we inspect its matrix form Z in (25): 1) . It is easy to find that Z has a sparse linear atomic representation over the following matrix-form atom set of infinite size:…”

Section: B Rr-based 2d MMV Via Customized D-anmmentioning

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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Section: A Redundancy-reduction Transformationmentioning

confidence: 99%

Section: B Rr-based 2d MMV Via Customized D-anmmentioning

confidence: 99%

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

Wang

Tian

Leus

et al. 2022

IEEE Trans. Signal Process.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Several studies have investigated strategies to compute the atomic norm such that the computational complexity increases linearly with the number of dimensions (see e.g. [35,36,37]).…”

Section: Non-rigid Wallsmentioning

confidence: 99%