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中文摘要：
信号重构是压缩感知理论的关键组成部分，研究快速有效的重构算法具有现实意义。目前，迭代阈值算法中的不动点迭代（FPC）算法，在重构速度和精度方面存在很大的提升空间。为此，文中首先提出了一种快速不动点迭代（FFPC）算法。接着针对该算法，通过引入子空间优化，充分利用压缩感知贪婪算法和凸优化算法的各自优点，提出了快速不动点一活动集（FFPC—AS）算法，进而得到更加准确的解。对于FFPC—AS算法，给出了收缩阶段和子空间优化阶段交替执行方案，避免了除偏（Debiasing）操作。大量仿真对比实验表明，所提算法既能快速重构图像信号，又可以提高准确率。
英文摘要：
Signal recovery is the key component of compressed sensing theory, which has practical significance to research the fast effective reconstruction algorithms. At present,the convergence rate and accuracy of Fixed Point Continuation （FPC） algorithm still can be improved. So, a Fast Fixed-Point Continuation （FFPC） algorithm is put forward f＇trsfly, and then it makes full use of the respective advantages of greedy algorithm and convex optimization by introducing subspace optimization to come up with the fast Fixed-Point Continuation_Active Set （ FFPC AS） algorithm, which can improve the accuracy and the convergence rate of FFPC algorithm. For the FFPC_ AS algorithm, the shrinkage phase and subspace optimization phase are performed repeatedly which can avoid the debiasing operatioli, and the embodiment of the two stages is given in this paper. A large number of comparative simulation results show that the proposed algorithm exhibits state-of-the-art performance in terms of both its speed and its ability to recover sparse signal.
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