Complete dictionary type stochastic sparse representation and its applications in random process simulation

This paper presents a sparse representation method for stochastic signals based on the complete dictionary constructed from the Szegő kernel. The study extends the theoretical framework proposed by Qian et al. By designing a complete dictionary of the Szegő kernel, we achieve an adaptive sparse expansion of stochastic signals. A rigorous convergence theorem is established, and a practical algorithm is developed. The proposed methodology is further applied to numerical simulations of stochastic processes, demonstrating significant advantages in the representation of random signals.