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- W4294190703 abstract "The goal of this short note is to present a refined analysis of the modified Basis Pursuit ($ell_1$-minimization) approach to signal recovery in Compressed Sensing with partially known support, as introduced by Vaswani and Lu. The problem is to recover a signal $x in mathbb R^p$ using an observation vector $y=Ax$, where $A in mathbb R^{ntimes p}$ and in the highly underdetermined setting $nll p$. Based on an initial and possibly erroneous guess $T$ of the signal's support ${rm supp}(x)$, the Modified Basis Pursuit method of Vaswani and Lu consists of minimizing the $ell_1$ norm of the estimate over the indices indexed by $T^c$ only. We prove exact recovery essentially under a Restricted Isometry Property assumption of order 2 times the cardinal of $T^c cap {rm supp}(x)$, i.e. the number of missed components." @default.
- W4294190703 created "2022-09-02" @default.
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- W4294190703 date "2009-06-02" @default.
- W4294190703 modified "2023-10-18" @default.
- W4294190703 title "On the modified Basis Pursuit reconstruction for Compressed Sensing with partially known support" @default.
- W4294190703 doi "https://doi.org/10.48550/arxiv.0906.0593" @default.
- W4294190703 hasPublicationYear "2009" @default.
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