中文摘要：

不动点连续（FPC）算法是一种凸优化算法，针对该算法收敛速度较慢的现象，提出了一种快速的不动点连续（FFPC）算法，算法引入线性搜索步长，选择合理的步长参数，利用前两次迭代结果的特殊线性组合值作为下次迭代的初始值，提高每次迭代的精度，从而加快收敛速度。FFPC算法的收敛性在实验中得到了验证，同时，仿真实验表明，FFPC算法的收敛速度有所提高，重构质量也比其他算法更好。

英文摘要：

Fixed Point Continuation （FPC） algorithm is a developed version of convex optimization algorithm, which is an important research method for reconstruction of Compressed Sensing （CS）. In this paper, a fast FPC （FFPC） algorithm is proposed to accel- erate the convergence speed of FPC algorithm. A linear search step is introduced, and then an efficient coefficient of shifting step is chosen, finally current iteration is updated by using special linear combination of two previous iterations, so the accuracy of each it- eration is improved, and hence the convergence speed is accelerated. On the one hand, the convergence of FFPC algorithm has been proved in the experiment, on the other hand, the simulation experiments show that the convergence speed of FFPC algorithm is obviously improved, and the reconstruction quality is better than other algorithms.