Time-frequency signature reconstruction from random observations using multiple measurement vectors

A new approach for sparse nonstationary signal reconstruction based on multiple windows is introduced. Signals which are localizable in the time-frequency (TF) domain give rise to sparsity in the same domain. When combined, sparse reconstructions, applied to randomly sampled data and corresponding to different selected windows, provide enhanced TF signature estimation. Among possible orthogonal windows, we consider those which characterize the eigen-decomposition of reduced-interference quadratic time-frequency distribution kernels. The highly overlapping TF support of the windows´ full-data spectrograms inspires the use of the multiple measurement vectors, in lieu of individual windowed signal recovery. It is shown that the proposed approach outperforms other reconstruction methods when only a single window is applied and is superior to reduced interference time-frequency distributions of random observations.