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Algorithm Performance Analysis for Reconstruction of Sparse Time-Frequency Distributions from Compressive Sensed Ambiguity Function

Time-frequency distributions (TFDs) are powerful tools for analysis of nonstationary signals, which allow us to observe signal energy distribution as a function of both time and frequency simultaneously. However, TFDs are often corrupted with artifacts, a mathematical byproduct of TFD quadratic nature. One method for their elimination is compressive sensing (CS) of signal ambiguity function (AF) in such a way to discard corrupted samples, leaving only a small subset of artifact-free samples. In order to obtain a high-resolution TFD, one needs to solve an optimization problem, namely the basis pursuit. In this paper, we perform a comparison of existing algorithms for solving unconstrained optimization problems, adapted for reconstruction of a TFD from a small number of CS-AF samples.

Time-frequency representation; Instantaneous frequency estimation; Signal sparsity; Compressive sensing; Basis pursuit; Linear unconstrained optimization.

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