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- W2938020605 abstract "We consider the problem of stable recovery of sparse signals of the form $$F(x)=sum_{j=1}^d a_jdelta(x-x_j),quad x_jinmathbb{R},;a_jinmathbb{C}, $$ from their spectral measurements, known in a bandwidth $Omega$ with absolute error not exceeding $epsilon>0$. We consider the case when at most $ple d$ nodes ${x_j}$ of $F$ form a cluster whose extent is smaller than the Rayleigh limit ${1overOmega}$, while the rest of the nodes are well separated. Provided that $epsilon lessapprox SRF^{-2p+1}$, where $SRF=(OmegaDelta)^{-1}$ and $Delta$ is the minimal separation between the nodes, we show that the minimax error rate for reconstruction of the cluster nodes is of order ${1overOmega}SRF^{2p-1}epsilon$, while for recovering the corresponding amplitudes ${a_j}$ the rate is of the order $SRF^{2p-1}epsilon$. Moreover, the corresponding minimax rates for the recovery of the non-clustered nodes and amplitudes are ${epsilonoverOmega}$ and $epsilon$, respectively. These results suggest that stable super-resolution is possible in much more general situations than previously thought. Our numerical experiments show that the well-known Matrix Pencil method achieves the above accuracy bounds." @default.
- W2938020605 created "2019-04-25" @default.
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- W2938020605 date "2019-04-19" @default.
- W2938020605 modified "2023-09-27" @default.
- W2938020605 title "Super-resolution of near-colliding point sources" @default.
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