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- W4287812827 abstract "In this paper we extend the deterministic sublinear FFT algorithm in Plonka et al. (2018) for fast reconstruction of $M$-sparse vectors ${mathbf x}$ of length $N= 2^J$, where we assume that all components of the discrete Fourier transform $hat{mathbf x}= {mathbf F}_{N} {mathbf x}$ are available. The sparsity of ${mathbf x}$ needs not to be known a priori, but is determined by the algorithm. If the sparsity $M$ is larger than $2^{J/2}$, then the algorithm turns into a usual FFT algorithm with runtime ${mathcal O}(N log N)$. For $M^{2} < N$, the runtime of the algorithm is ${mathcal O}(M^2 , log N)$. The proposed modifications of the approach in Plonka et al. (2018) lead to a significant improvement of the condition numbers of the Vandermonde matrices which are employed in the iterative reconstruction. Our numerical experiments show that our modification has a huge impact on the stability of the algorithm. While the algorithm in Plonka et al. (2018) starts to be unreliable for $M>20$ because of numerical instabilities, the modified algorithm is still numerically stable for $M=200$." @default.
- W4287812827 created "2022-07-26" @default.
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- W4287812827 date "2020-04-23" @default.
- W4287812827 modified "2023-09-26" @default.
- W4287812827 title "Deterministic Sparse Sublinear FFT with Improved Numerical Stability" @default.
- W4287812827 hasPublicationYear "2020" @default.
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