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This paper is concerned with estimating unknown multidimensional frequencies from linear compressive measurements. This is accomplished by employing the recently proposed atomic norm minimization framework to recover these frequencies under a sparsity prior without imposing any grid restriction on these frequencies. To this end, we give a rigorous derivation of an iterative scheme called alternating direction of multipliers method, which is able to incorporate multiple compressive snapshots from a multi-dimensional superposition of complex harmonics.

It is known that the calculation of a matrix–vector product can be accelerated if this matrix can be recast (or approximated) by the Kronecker product of two smaller matrices. In array signal processing, the manifold matrix can be described as the Kronecker product of two other matrices if the sensor array displays a separable geometry. This forms the basis of the Kronecker Array Transform (KAT), which was previously introduced to speed up the calculations of acoustic images with microphone arrays.

Identifying characteristic vibrational modes and frequencies is of great importance for monitoring the health of structures such as buildings and bridges. In this work, we address the problem of estimating the modal parameters of a structure from small amounts of vibrational data collected from wireless sensors distributed on the structure. We consider a randomized spatial compression scheme for minimizing the amount of data that is collected and transmitted by the sensors.

This work investigates the parameter estimation performance of super-resolution line spectral estimation using atomic norm minimization. The focus is on analyzing the algorithm's accuracy of inferring the frequencies and complex magnitudes from noisy observations. When the Signal-to-Noise Ratio is reasonably high and the true frequencies are separated by $O(\frac{1}{n})$, the atomic norm estimator is shown to localize the correct number of frequencies, each within a neighborhood of size $O(\sqrt{\frac{\log n}{n^3}} \sigma)$ of one of the true frequencies.

We consider the problem of geolocating two unknown co-channel emitters by a cluster of formation-flying satellites using both time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements. As the association between the TDOA/FDOA measurements obtained by each pair of satellites and the corresponding emitters is typically not known, the emitter-measurement association and the emitters' locations need to be jointly estimated. In this paper, we first formulate the joint estimation problem as a mixed integer nonlinear optimization problem.