Full Program »
A compressive sensing based framework for evolutionary power spectrum estimation subject to missing data
Accurate evolutionary power spectrum estimation can provide invaluable stochastic process information in the joint time-frequency domain. To this end, real sensory data are often required corresponding to such processes from which the spectrum can be estimated. Unfortunately, if these data records are not evenly sampled without gaps (i.e. some data are missing), there arise significant difficulties with standard spectral analysis techniques. Situations in which missing data may occur are numerous and often unpredictable. Equipment failure or restricted use of equipment can lead to gaps, as well as data corruption and cost / bandwidth limitations to name just a few. In this regard, a compressive sensing (CS) based framework is presented for estimating the power spectrum when faced with these problematic cases. First, an appropriate basis is defined based on practical knowledge of similar processes. Then, by minimizing the L1-norm of the sampled data mapped onto the new basis, the sparsest representation can be found. In cases where an ensemble of stochastic process realizations are assumed to be available, standard CS techniques may be combined with an adaptive basis reweighting procedure to vastly improve spectrum estimation accuracy. Power spectrum estimates can then be derived from the new coefficients directly in cases where Fourier or Harmonic Wavelet bases are utilized, or by applying any preferred spectrum estimation procedure once the signal is reconstructed otherwise. The techniques are shown to identify dominant spectral peaks in recorded processes with significant levels of missing data accurately, beyond the point where other commonly used techniques become redundant. Further, a significant advantage of these approaches relates to the fact that they behave satisfactorily even in the presence of noise.Author(s):
Liam Comerford
Institute for Risk and Uncertainty, University of Liverpool, UK
United Kingdom
Ioannis Kougioumtzoglou
Columbia University, New York, USA
United States
Michael Beer
Institute for Risk and Uncertainty, University of Liverpool, UK
United Kingdom