An accelerated class of adaptive scheme of iterative thresholding algorithms is studied analytically and empirically. They are based on the feedback mechanism of the null space tuning techniques. The main contribution of this article is the accelerated convergence analysis and proofs with a variable/adaptive index selection and different feedback principles at each iteration. The convergence analysis requires no longer a priori sparsity information $s$ of a signal. It is shown that uniform recovery of all $s$-sparse signals from given linear measurements can be achieved under reasonable (preconditioned) restricted isometry conditions. Accelerated convergence rate and improved convergence conditions are obtained by selecting an appropriate size of the index support per iteration. The theoretical findings are sufficiently demonstrated and confirmed by extensive numerical experiments. It is also observed that the proposed algorithms have a clearly advantageous balance of efficiency, adaptivity and accuracy compared with all other state-of-the-art greedy iterative algorithms.

对迭代阈值算法的自适应方案的加速类进行了分析和经验研究。它们基于零空间调谐技术的反馈机制。本文的主要贡献是在每次迭代中使用可变/自适应索引选择和不同的反馈原则进行加速收敛分析和证明。收敛分析不再需要先验的稀疏信息$秒$的一个信号。结果表明，所有的均匀回收$秒$- 可以在合理（预处理）受限等距条件下实现来自给定线性测量的稀疏信号。通过每次迭代选择合适的索引支持大小，可以获得加速的收敛速度和改进的收敛条件。大量的数值实验充分证明和证实了理论发现。还观察到，与所有其他最先进的贪婪迭代算法相比，所提出的算法在效率、适应性和准确性之间具有明显的优势平衡。