Identification of Coupled Map Lattice Based on Compressed Sensing

A novel approach for the parameter identification of coupled map lattice (CML) based on compressed sensing is presented in this paper. We establish a meaningful connection between these two seemingly unrelated study topics and identify the weighted parameters using the relevant recovery algorithms in compressed sensing. Specifically, we first transform the parameter identification problem of CML into the sparse recovery problem of underdetermined linear system. In fact, compressed sensing provides a feasible method to solve underdetermined linear system if the sensing matrix satisfies some suitable conditions, such as restricted isometry property (RIP) and mutual coherence. Then we give a low bound on the mutual coherence of the coefficient matrix generated by the observed values of CML and also prove that it satisfies the RIP from a theoretical point of view. If the weighted vector of each element is sparse in the CML system, our proposed approach can recover all the weighted parameters using only about M samplings, which is far less than the number of the lattice elements N . Another important and significant advantage is that if the observed data are contaminated with some types of noises, our approach is still effective. In the simulations, we mainly show the effects of coupling parameter and noise on the recovery rate.