Adaptive L-Wigner Initialization for Sparse Time–Frequency Distribution Reconstruction

Compressed sensing (CS) applied in the ambiguity domain offers an effective approach for recovering time–frequency distributions (TFDs) of non-stationary signals from sparse representations. Existing methods predominantly rely on the Wigner–Ville distribution (WVD) as the initial representation due to its simplicity and high auto-term concentration. However, the WVD performs poorly for signals with higher-order frequency-modulated (FM) components and is highly sensitive to interference and noise, which then propagate into the reconstruction. This paper introduces the systematic use of the L-Wigner distribution (LWD) as the initial representation for CS-based reconstruction, providing front-end adaptability to signal characteristics. By generating a controllable family of TFDs ranging from the spectrogram to cross-term-free polynomial WVDs, the LWD enables effective suppression of interference and noise while simultaneously enhancing auto-term localization for nonlinear FM components. The proposed LWD-based reconstruction framework is evaluated against the conventional WVD-based method using several state-of-the-art reconstruction algorithms, whose parameters are jointly optimized through a multi-objective meta-heuristic framework to ensure a fair comparison. Experiments on noisy synthetic signals and real-world gravitational-wave data demonstrate consistent performance gains. On synthetic signals, the proposed approach reduces the average reconstruction error index by up to 36.6%, improves the ℓ1-reconstruction error by up to 75.8%, and achieves complete elimination of cross-term energy. In addition, robustness analysis under additive white Gaussian noise shows up to a 75% improvement in ℓ1 performance. For real gravitational-wave data, the method reduces the mean reconstruction index by up to 5.8% while maintaining auto-term preservation and eliminating cross-term artifacts. These results establish the LWD-based initialization as an effective and general strategy for TFD reconstruction in complex signal environments.