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On the noise impact in the L1 based reconstruction of the sparse time-frequency distributions

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 by artifacts, a mathematical byproduct of TFD quadratic nature. A method for artefact suppression is compressive sensing (CS) of signal ambiguity function (AF) in such a way to discard corrupted samples, and leaving only a small subset of artifact-free signal samples. However, in order to obtain a high-resolution TFD, one needs to solve a linear unconstrained optimization problem. In this paper, we analyse noise effect on TFD reconstruction based on various ℓ1 norm algorithms for different sizes of CSAF regions of interest.