Precise Semidefinite Programming Formulation of Atomic Norm Minimization for Recovering d-Dimensional ($d\geq 2$) Off-the-Grid Frequencies
This work addresses a foundational challenge in off-the-grid compressed sensing for researchers in signal processing, providing a theoretical framework for multi-dimensional frequency recovery.
The paper solves the open problem of formulating an equivalent semidefinite programming (SDP) formulation for atomic norm minimization to recover signals with d-dimensional (d≥2) off-the-grid frequencies, enabling precise recovery in compressed sensing.
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 ($d\geq 2$) 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 ($d\geq 2$) off-the-grid frequencies.