Abstract
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 π / 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.
Highlights
Signal decomposition and expression comprise a fundamental problem in the theory research and engineering application of signal processing
The traditional signal decomposition methods are decomposing the signals into a set of complete orthogonal bases, such as cosine transform bases, Fourier transform bases, wavelet transform bases, and so on
Mallat et al proposed a new signal decomposition method based on over-complete bases, which is called sparse decomposition or sparse reconstruction [2]
Summary
Signal decomposition and expression comprise a fundamental problem in the theory research and engineering application of signal processing. The traditional signal decomposition methods are decomposing the signals into a set of complete orthogonal bases, such as cosine transform bases, Fourier transform bases, wavelet transform bases, and so on. These decomposition methods suffer from inherent limitations for different kinds of signals [1]. Compared with complete orthogonal bases, the over-complete bases (or redundant dictionary) are redundant, that is the number of base elements is larger than that of the dimensions In this case, the orthogonality between the bases will no longer be guaranteed, and the bases are renamed atoms. Because the sparse decomposition can adaptively reconstruct the sparse signals using atoms in the dictionary, it has been widely applied in many aspects, such as signal
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