  Modal analysis is the process of estimating a system's modal parameters such
as its natural frequencies and mode shapes. One application of modal analysis
is in structural health monitoring (SHM), where a network of sensors may be
used to collect vibration data from a physical structure such as a building or
bridge. There is a growing interest in developing automated techniques for SHM
based on data collected in a wireless sensor network. In order to conserve
power and extend battery life, however, it is desirable to minimize the amount
of data that must be collected and transmitted in such a sensor network. In
this paper, we highlight the fact that modal analysis can be formulated as an
atomic norm minimization (ANM) problem, which can be solved efficiently and in
some cases recover perfectly a structure's mode shapes and frequencies. We
survey a broad class of sampling and compression strategies that one might
consider in a physical sensor network, and we provide bounds on the sample
complexity of these compressive schemes in order to recover a structure's mode
shapes and frequencies via ANM. A main contribution of our paper is to
establish a bound on the sample complexity of modal analysis with random
temporal compression, and in this scenario we prove that the samples per sensor
can actually decrease as the number of sensors increases. We also extend an
atomic norm denoising problem to the multiple measurement vector (MMV) setting
in the case of uniform sampling.
