Compressive recovery of 2-D off-grid frequencies

Abstract

Estimation of two-dimensional frequencies arises in many applications such as radar, inverse scattering, and wireless communications. In this paper, we consider retrieving continuousvalued two-dimensional frequencies in a mixture of r complex sinusoids from a random subset of its n regularly-spaced timedomain samples. We formulate an atomic norm minimization program that, with high probability, guarantees perfect recovery from O(r log r log n) samples under a mild frequency separation condition. We propose to solve the atomic norm minimization via semidefinite programming, and validate the proposed algorithm via numerical examples. Our work extends the framework proposed by Tang et. al.[1] for line spectrum estimation to multidimensional spectrum estimation.

Robust Spectral Compressed Sensing via Structured Matrix Completion

“…Proof: See Appendix C. Recognizing that (35) is the same as (27), the following proof also establishes Theorem 4. Note that Lemma 2 immediately leads to…”

Compressive Two-Dimensional Harmonic Retrieval via Atomic Norm Minimization

“…Specifically, consider a time-domain signal of ambient dimension , composed of distinct 2-D complex sinusoids. If the frequencies of the sinusoids lie approximately on the fine DFT grid of the normalized frequency plane [0, 1) [0,1), the signal of interest can be sparsely represented over the DFT basis. It has been demonstrated that the signal can be recovered from a random subset of time-domain samples with a sample size of [14] via basis pursuit [15] or greedy pursuit [16].…”

Compressed sensing applied to weather radar

“…This grid-free approach is inspired by the problems of total variation minimization (Candès and Fernandez-Granda 2013) and atomic norm minimization (Tang et al 2013b) to recover super-resolution frequencieslying anywhere in the continuous domain [0,1] -with few random time samples of the spectrally sparse signal, provided the line spectrum maintains a nominal separation. A number of generalizations of off-the-grid compressed sensing for specific signal scenarios have also been attempted, including extension to higher dimensions (Chi and Chen 2013;Chi et al 2011;Xu et al 2014;Yang and Xie 2014).…”