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A simultaneous sparse approximation method for multidimensional harmonic retrieval
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DOI：10.1016/j.sigpro.2016.07.029.png)
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Abstract
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In this paper, a new method for the estimation of the parameters of multidimensional (R-D) harmonic and damped complex signals in noise is presented. The problem is formulated as R simultaneous sparse approximations of multiple 1-D signals. To get a method able to handle large size signals while maintaining a sufficient resolution, a multigrid dictionary refinement technique is associated to the simultaneous sparse approximation. The refinement procedure is proved to converge in the single R-D mode case. Then, for the general multiple modes case, the signal tensor model is decomposed in order to handle each mode separately in an iterative scheme. The proposed method does not require an association step since the estimated modes are automatically paired. We also derive the Cramer-Rao lower bounds of the parameters of modal R-D signals. The expressions are given in compact form in the single tone case. Finally, numerical simulations are conducted to demonstrate the effectiveness of the proposed method. (C) 2016 Elsevier B.V. All rights reserved.
Keywords:
Multidimensional harmonic retrieval
Frequency estimation
Simultaneous sparse approximation
Multigrid dictionary refinement
Cramer-Rao lower bound
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Deterministic asymptotic Cramer-Rao bound for the multidimensional harmonic model.png)
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