A Sparse Signal Reconstruction Method Based on Improved Double Chains Quantum Genetic Algorithm

This paper proposes a novel method of sparse signal reconstruction, which combines the improved double chains quantum genetic algorithm (DCQGA) and the orthogonal matching pursuit algorithm (OMP). Firstly, aiming at the problems of the slow convergence speed and poor robustness of traditional DCQGA, we propose an improved double chains quantum genetic algorithm (IDCQGA). The main innovations contain three aspects: (1) a high density quantum encoding method is presented to reduce the searching space and increase the searching density of the algorithm; (2) the adaptive step size factor is introduced in the chromosome updating, which changes the step size with the gradient of the objective function at the search points; (3) the quantum $\pi /6$ -gate is proposed in chromosome mutation to overcome the deficiency of the traditional NOT-gate mutation with poor performance to increase the diversity of the population. Secondly, for the problem of the OMP algorithm not being able to reconstruct precisely the effective sparse signal in noisy environments, a fidelity orthogonal matching pursuit (FOMP) algorithm is proposed. Finally, the IDCQGA-based OMP and FOMP algorithms are applied to the sparse signal decomposition, and the simulation results show that the proposed algorithms can improve the convergence speed and reconstruction precision compared with other methods in the experiments.