Local sparse reconstructions of Doppler frequency using chirp atoms

The paper considers sparse reconstruction of Doppler and microDoppler time-frequency (TF) signatures of radar returns of moving targets from limited or incomplete data. The typically employed sinusoidal dictionary, relating the windowed compressed measurements to the signal local frequency contents, induces competing requirements on the window size. In this paper, we use chirp dictionary for each window position to relax this adverse window length-sparsity interlocking. It is shown that local frequency reconstruction using chirp atoms better represents the approximate piece-wise chirp behavior of most Doppler TF signatures. This enables the utilization of longer windows for accurate time-frequency representations. Simulation examples are provided demonstrating the superior performance of local chirp dictionary over its sinusoidal counterpart.