基于粒子群优化的稀疏分解变尺度快速算法

针对一类可分稀疏性度量函数，结合最优化理论,研究了稀疏信号重构的快速算法。稀疏分解可以看成是一个带等式约束的优化问题，首先利用惩罚函数法将其转化为无约束优化问题|然后在粒子群优化估计搜索步长的基础上，利用变尺度法寻找无约束优化问题的最优解|最后依次增大惩罚因子，直至稀疏表示系数满足分解精度的要求。该算法避免了矩阵求逆运算，且无需先验地选取惩罚因子。仿真实验验证了算法的有效性和快速性。

Fast variable matrix algorithm for sparse decomposition based on PSO

For a class of separable sparsity-measure functions,a fast algorithm for the reconstruction of sparse signals is researched based on the optimization theory.The sparse decomposition is regarded as an optimization problem with constrained equations.Firstly,it is transformed to a nonconstraint optimization problem using the penalty function method.Then,based on the estimation of the search step via particle swarm optimization,the variable matrix method is used to search the solution for the problem.Finally,the penalty factor is gradually augmented until the sparse coefficients meet the demand of decomposition precision.In the proposed algorithm,the matrix inversion operation is avoided,and it is unnecessary to choose the penalty factor in apriority.The availability and rapidity of the algorithm is validated by simulation experiment.