基于压缩感知的加速前向后向匹配追踪算法

Acceleration Forward-backward Pursuit Algorithm Based on Compressed Sensing

前向后向匹配追踪(FBP)算法作为一个新颖的两阶段贪婪逼近算法,因为较高的重构精度和不需要稀疏度作为先验信息的特点,受到了人们的广泛关注。然而,FBP算法必须运行更多的时间才能得到更高的精度。鉴于此,该文提出加速前向后向匹配追踪(AFBP)算法。该算法利用每次迭代中候选支撑集的信息,实现对已删除原子的再次加入,以此减少算法迭代次数。通过不同非零项分布的稀疏信号和稀疏图像的仿真结果表明,相对于FBP算法,该文提出的方案在不降低重构精度的同时,大幅降低了算法运行时间。

The Forward-Backward Pursuit （FBP） algorithm, a novel two stage greedy approach, receives wide attention due to the high reconstruction accuracy and the feature without prior information of the sparsity. However, FBP has to run more time to get a higher precision. To alleviate this drawback, this paper proposes the Acceleration Forward-Backward Pursuit （AFBP） algorithm based on Compressed Sensing （CS）. In order to reduce the number of iterations, the algorithm exploits the information available in the support estimate to add the deleted atoms again. The run time of AFBP is sharply shorter than that of FBP, while the precision of AFBP is not lower than FBP. The efficacy of the proposed scheme is demonstrated by simulations using random sparse signals with different nonzero coefficient distributions and a sparse image.