Time-frequency signature sparse reconstruction using chirp dictionary

Abstract

This paper considers local sparse reconstruction of time-frequency signatures of windowed non-stationary radar returns. These signals can be considered instantaneously narrow-band, thus the local time-frequency behavior can be recovered accurately with incomplete observations. The typically employed sinusoidal dictionary induces competing requirements on window length. It confronts converse requests on the number of measurements for exact recovery, and sparsity. In this paper, we use chirp dictionary for each window position to determine the signal instantaneous frequency laws. This approach can considerably mitigate the problems of sinusoidal dictionary, and enable the utilization of longer windows for accurate time-frequency representations. It also reduces the picket fence by introducing a new factor, the chirp rate α. Simulation examples are provided, demonstrating the superior performance of local chirp dictionary over its sinusoidal counterpart.

Simplified chirp dictionary for time-frequency signature sparse reconstruction of radar returns

“…2(a) that cross-terms and noise-like artifacts clutter the signal component and hide the pertinent signal structure when the WVD is employed. The sinusoidal dictionary approach reveals inaccuracy in the TF signature estimation since besides insufficient sparsity, it is vulnerable to the picket fence effect [26], resulting in frequency contents at false locations. The chirp dictionary approach can address this failure and the instantaneous frequency laws are resolved as seen in Fig.…”

“…This task is carried out by CS techniques with a full chirp atom Ψ F . The parameter space of interest is [25], [26]:…”

“…Note that the "˜" refers to "dictionary values". The full chirp dictionary Ψ F is defined as [25], [26]:…”

“…In this respect, they are sparse in the joint time-frequency domain. Thus, the segments' time-frequency signature can be recovered by sparse reconstruction with the measurement dictionary being chirp atoms [25], [26]. Greedy algorithms or convex optimization techniques are used to obtain the sparsest chirp combination that best describes the windowed signals.…”

Sparse reconstruction of time-frequency representation using the fractional Fourier transform

“…However, this approach means contradictory demands on the number of measurements for exact recovery and sparsity. It also suffers from the picket fence effect [5]. Now, the chirp approach can mitigate these issues, and obtain more accurate approximation by deploying chirp atoms for each window position to determine the signal's instantaneous frequency [6].…”