论文标题
部分可观测时空混沌系统的无模型预测
Heavy-Ball-Based Hard Thresholding Algorithms for Sparse Signal Recovery
论文作者
论文摘要
硬阈值技术在稀疏信号恢复算法的发展中起着至关重要的作用。通过合并这项技术和重力加速方法，该方法是传统梯度下降方法的多步扩展，我们提出了所谓的基于重的强球硬阈值（HBHT）（HBHT）和基于重球的硬阈值Passuit（HBHTP）算法，以进行信号回收。事实证明，如果测量矩阵的限制等轴测常数满足$δ_{3K} <0.618 $和$δ__{3K {3K} <0.577， $，则HBHT和HBHTP可以成功恢复$ K $ -SPARSE信号。在$δ_{2K} <0.356 $和$δ_{2k} <0.377，$的条件下，HBHT和HBHTP的保证成功也显示在$δ__{2K} <0.356 $中。此外，本文还建立了两种算法的有限收敛性和稳定性。进行随机问题实例的模拟，以比较提出的算法的性能和几种现有算法的性能。经验结果表明，HBHTP与一些现有算法相当可观，并且与这些现有方法相比，实现信号恢复的平均时间少。
The hard thresholding technique plays a vital role in the development of algorithms for sparse signal recovery. By merging this technique and heavy-ball acceleration method which is a multi-step extension of the traditional gradient descent method, we propose the so-called heavy-ball-based hard thresholding (HBHT) and heavy-ball-based hard thresholding pursuit (HBHTP) algorithms for signal recovery. It turns out that the HBHT and HBHTP can successfully recover a $k$-sparse signal if the restricted isometry constant of the measurement matrix satisfies $δ_{3k}<0.618 $ and $δ_{3k}<0.577,$ respectively. The guaranteed success of HBHT and HBHTP is also shown under the conditions $δ_{2k}<0.356$ and $δ_{2k}<0.377,$ respectively. Moreover, the finite convergence and stability of the two algorithms are also established in this paper. Simulations on random problem instances are performed to compare the performance of the proposed algorithms and several existing ones. Empirical results indicate that the HBHTP performs very comparably to a few existing algorithms and it takes less average time to achieve the signal recovery than these existing methods.
