This paper introduces a novel Knockoff-guided compressive sensing framework, referred to as \TheName{}, which enhances signal recovery by leveraging precise false discovery rate (FDR) control during the support identification phase. Unlike LASSO, which jointly performs support selection and signal estimation without explicit error control, our method guarantees FDR control in finite samples, enabling more reliable identification of the true signal support. By separating and controlling the support recovery process through statistical Knockoff filters, our framework achieves more accurate signal reconstruction, especially in challenging scenarios where traditional methods fail. We establish theoretical guarantees demonstrating how FDR control directly ensures recovery performance under weaker conditions than traditional $\ell_1$-based compressive sensing methods, while maintaining accurate signal reconstruction. Extensive numerical experiments demonstrate that our proposed Knockoff-based method consistently outperforms LASSO-based and other state-of-the-art compressive sensing techniques. In simulation studies, our method improves F1-score by up to 3.9x over baseline methods, attributed to principled false discovery rate (FDR) control and enhanced support recovery. The method also consistently yields lower reconstruction and relative errors. We further validate the framework on real-world datasets, where it achieves top downstream predictive performance across both regression and classification tasks, often narrowing or even surpassing the performance gap relative to uncompressed signals. These results establish \TheName{} as a robust and practical alternative to existing approaches, offering both theoretical guarantees and strong empirical performance through statistically grounded support selection.

翻译：本文提出了一种新颖的Knockoff引导的压缩感知框架（简称\TheName{}），该框架通过在支撑集识别阶段利用精确的错误发现率（FDR）控制来增强信号恢复。与LASSO联合执行支撑集选择和信号估计但缺乏显式误差控制不同，我们的方法在有限样本下保证FDR控制，从而能够更可靠地识别真实信号的支撑集。通过统计Knockoff滤波器分离并控制支撑集恢复过程，我们的框架实现了更准确的信号重建，尤其是在传统方法失效的挑战性场景中。我们建立了理论保证，证明在比传统基于$\ell_1$范数的压缩感知方法更弱的条件下，FDR控制如何直接确保恢复性能，同时保持准确的信号重建。大量的数值实验表明，我们提出的基于Knockoff的方法在性能上持续优于基于LASSO的方法及其他先进的压缩感知技术。在模拟研究中，得益于原则性的错误发现率（FDR）控制和增强的支撑集恢复能力，我们的方法将F1分数较基线方法提升了最高达3.9倍。该方法还持续产生更低的重建误差和相对误差。我们进一步在真实世界数据集上验证了该框架，其在回归和分类任务中均取得了最优的下游预测性能，常常缩小甚至超越了相对于未压缩信号的性能差距。这些结果确立了\TheName{}作为现有方法的一个鲁棒且实用的替代方案，通过基于统计的支撑集选择，既提供了理论保证，又展现了强大的实证性能。