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To achieve a high-resolution modal estimation, a possible way is to define a high resolution dictionary often resulting in a prohibitive computational burden.
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where A is an M × F Vandermonde matrix: A = 1 1 ⋯ 1 a 1 a 2 ⋯ a F a 1 2 a 2 2 ⋯ a F 2 ⋮ ⋮ ⋮ a 1 M - 1 a 2 M - 1 ⋯ a F M - 1. and c = [c1,...,c F ] T. The problem of modal estimation is an inverse problem since y is given and A,c, and F are unknown.
In particular, we can envisage to used multiple 1-D modal estimation to get a low dimension initial dictionary for R-D modal estimation.
Then the modal estimation problem can be formulated as a penalized ℓ2 - ℓ0 sparse signal estimation problem (2).
A special case of modal estimation is the harmonic retrieval problem (null damping factor) which has been formulated as a sparse approximation in a number of contributions.
We address the problem of multidimensional modal estimation using sparse estimation techniques coupled with an efficient multigrid approach.
Sahnoun et al. [8] address multi-dimensional modal estimation using sparse estimation techniques in combination with an efficient multigrid approach.
In this section, we present some experimental results for the multigrid sparse modal estimation.
In Section 5, we extend the sparse multigrid approach to the R-D modal estimation problem.
(iii) We show how to extend the sparse 1-D modal estimation problem to R-D modal problems.
The goal of this article is to present an efficient approach that reduces the computational cost of sparse algorithms for R-D modal estimation problems.
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