Continuous structure based Bayesian compressive sensing for sparse reconstruction of time-frequency distributions

In this paper, we propose a Bayesian compressive sensing algorithm for effective reconstruction of sparse signals that demonstrate sparsity as continuous but irregular narrow strips in a multi-dimensional space. Among many applications of this class of representations are the two-dimensional time-frequency distributions (TFDs) of radar signals, which are often modeled as frequency modulated (FM) signals characterized by their sparse and continuous instantaneous frequencies. A spike-and-slab prior is introduced to statistically encourage sparsity of the time-frequency representations (TFRs) across each segmented time-frequency region, and a patterned prior is imposed to enforce the continuous structure of the TFR. Compared with the existing sparse signal reconstruction techniques, the proposed technique achieves improved interpretation of the TFD, particularly when the signals are noisy or with missing samples.