Reduced interference time-frequency representations and sparse reconstruction of undersampled data

In this paper, we examine the time-frequency representation (TFR) and sparse reconstruction of non-stationary signals in the presence of missing data samples. These samples lend themselves to missing entries in the instantaneous auto-correlation function (IAF) which, in turn, induce artifacts in the time-frequency distribution and ambiguity function. The artifacts are additive noise-like and, as such, can be mitigated by using proper time-frequency kernels. We show that the sparse signal reconstruction methods applied to the time-lag domain improve the TFR over the direct application of Fourier transform to the IAF. Additionally, the paper demonstrates that the use of signal-adaptive kernels provides superior performance compared to data-independent kernels when missing data are present.