Precise Semidefinite Programming Formulation of Atomic Norm Minimization for Recovering d-Dimensional ($d\ge 2$) Off-the-Grid Frequencies

Abstract

Recent research in off-the-grid compressed sensing (CS) has demonstrated that, under certain conditions, one can successfully recover a spectrally sparse signal from a few time-domain samples even though the dictionary is continuous. In particular, atomic norm minimization was proposed in \cite{tang2012csotg} to recover $1$-dimensional spectrally sparse signal. However, in spite of existing research efforts \cite{chi2013compressive}, it was still an open problem how to formulate an equivalent positive semidefinite program for atomic norm minimization in recovering signals with $d$-dimensional ($d\ge 2$) off-the-grid frequencies. In this paper, we settle this problem by proposing equivalent semidefinite programming formulations of atomic norm minimization to recover signals with $d$-dimensional ($d\ge 2$) off-the-grid frequencies.

4 pages, double-column,1 Figure

References in corpus (1)

• Compressed Sensing off the Grid

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