<p>Compressive sensing (CS) is an innovative data processing framework that directly collects a limited number of samples as compressed signals and reconstructs the complete signal using sparsity-based optimization algorithms. CS can enhance the sampling efficiency of structural vibration sensors, mitigating challenges related to energy storage and bandwidth constraints. This paper presents an improved multi-task spectral CS approach specifically designed for structural vibration signals, addressing two key issues. First, spectral leakage effects often reduce signal sparsity in the frequency domain, resulting in suboptimal performance of traditional CS algorithms. To address this, we employ a spectral CS framework incorporating a redundant Fourier dictionary and a coherence-inhibiting selection mechanism, thereby mitigating spectral leakage effects and achieving superior reconstruction performance. Second, our approach leverages common sparsity patterns among vibration signals collected from multiple sensors, further enhancing overall reconstruction performance. The effectiveness of the proposed method is validated using both simulated data from a Kiewitt dome and field data from the Jiashao Bridge. Comparative experiments demonstrate the superiority of our approach over the traditional single-task CS methods and a recent multi-task CS method. Key algorithm parameters (i.e., sparsity level, frequency redundancy indicator, the coherence tolerance, and iteration step) are systematically investigated, and recommended settings are provided to guide practical implementation.</p>