Research On Sparse Decomposition Algorithms Based On Population Optimization

Signal sampling is the bridge between analog source signal and digital signal.According to the classical Shannon sampling theorem, the sampling frequency shouldbe not less than twice the maximum frequency of the signal, in order to recover thesignal without distortion. With the rapid progress of information technologies, thedemands for information are increasing dramatically. In recent years, an emergingtheorem of signal acquirement—compressed sensing (CS) provides an opportunityfor solving this problem. CS theory samples signal with far less than the rate requiredby the Shannon’s sampling theorem, and the signal can be fully restored with a highprobability, this means that the signal sampling and processing can be carried out at avery low rate. In order to ensure the accuracy of compressed sensing signalreconstruction, the core is to find the best signal sparse domain.And that is signalsparse decomposition, which is the basis and premise of the theory. But high timecomplexity has been the bottleneck of the signal sparse decomposition. Although theMP algorithm is the most classic signal sparse decomposition algorithm, the amountof computation is still huge. For the lack of the MP algorithm, this paper completedthe following two aspects based on intelligent algorithms:(1) Research on MP algorithm based on ant colony optimization: First, transferthe process that the MP algorithm each time selects the best atom from aover-complete library into an approximate solution by ant colony algorithm. The formof the solution in the ant colony algorithm is then set to a vector consisting of the fourcontrol parameters of the atoms in the complete dictionary. And treat the absolutevalue of the inner product of the signal or residual atoms as the objective function.According to the specific characteristics of MP algorithm, the pheromonematrix,pheromone local update and global update in the ant colony algorithm aredesigned in detail. Experimental results show this algorithm guarantees the signalreconstruction accuracy,at the same time, the decomposition rate is several dozenstimes higher than the classical MP algorithm.And It improves the operating efficiencyof the algorithm effectively.(2) Research on MP algorithm based on genetic algorithm: using geneticalgorithm to complete the iterative selection of the best atomic in MP algorithm.Specific methods are as follows: treat the discretization parameter group of the atomsin the dictionary as the chromosome of genetic algorithm; treat the absolute value ofthe inner product of the signal or residual atoms as the fitness function; And then designed the offspring generation mechanism of genetic algorithm according to thespecific characteristics of the problem. Experimental results show that the algorithmthe classic MP algorithm has a better time efficiency.This paper researches mainly signal sparse decomposition algorithm incompressed sensing. The work not only enriches the theoretical study of signal sparsedecomposition algorithm, but also improves the operating efficiency of the MPalgorithm.