Abstract:

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.