Abstract: Signal reconstruction is one of the core technologies of compressed sensing, and the reconstruction accuracy and time-consuming directly affects its application effect. Nowadays, Stagewise Orthogonal Matching Pursuit （StOMP） algorithm has been widely used for short running time, but its reconstruction accuracy is unsatisfactory. To make up for the defects of the StOMP algorithm, this paper presents a variant of StOMP, called backtracking-based adaptive and inertia weight index decreasing particle swarm optimization-based StOMP（ba-IWPSO-StOMP） algorithm. As an extension of the StOMP algorithm, in each iteration, the proposed ba-IWPSO-StOMP algorithm incorporates a backtracking technique to select atoms by the second screening, then uses the IWPSO algorithm to optimize atoms in the measurement matrix. Through these modifications, the ba-IWPSO-StOMP algorithm achieves superior reconstruction accuracy and less times of iteration compared with other OMP-type algorithms. Moreover, unlike its predecessors, the ba-IWPSO-StOMP algorithm does not require to know the sparsity level in advance. The experiments demonstrate the performance of ba-IWPSO-StOMP algorithm is superior to several other OMP-type algorithms.

Key words: compressed sensing, Stagewise Orthogonal Matching Pursuit（StOMP）, Particle Swarm Optimization（PSO）

摘要： 信号重构是压缩感知的核心技术之一，而其重构精度和所耗时长直接影响其应用效果。现今分段正交匹配追踪算法（StOMP）因耗时短而得到广泛应用，但也存在着重构精度差、稳定性低的缺点。提出一种基于粒子群优化（PSO）算法且同时具有回溯特性的StOMP改进算法（ba-IWPSO-StOMP），即首先在StOMP算法的一次原子选择上，引入回溯策略，实现原子的二次筛选；在每次迭代计算中，使用具有惯性权重指数递减的PSO（IWPSO）算法对传感矩阵中部分原子进行优化，从而实现更高精度，更少迭代次数的信号重构。对一维信号和二维图像的重构结果表明，在稀疏条件相同的情况下，算法在收敛时间较短的情况下，其重构精度明显优于StOMP等同类算法。

关键词: 压缩感知, 分段正交匹配追踪, 粒子群优化