Compressive sensing for power spectrum estimation of multi-dimensional processes under missing data

A compressive sensing (CS) based approach is applied in conjunction with an adaptive basis re-weighting procedure for multi-dimensional stochastic process power spectrum estimation. In particular, the problem of sampling gaps in stochastic process records, occurring for reasons such as sensor failures, data corruption, and bandwidth limitations, is addressed. Specifically, due to the fact that many stochastic process records such as wind, sea wave and earthquake excitations can be represented with relative sparsity in the frequency domain, a CS framework can be applied for power spectrum estimation. By relying on signal sparsity, and the assumption that multiple records are available upon which to produce a spectral estimate, it has been shown that a re-weighted CS approach succeeds in estimating power spectra with satisfactory accuracy. Of key importance in this paper is the extension from one-dimensional vector processes to a broader class of problems involving multidimensional stochastic fields. Numerical examples demonstrate the effectiveness of the approach when records are subjected to up to 75% missing data.