A modified parallel monotone hybrid algorithm for a finite family of $\mathcal{G}$-nonexpansive mappings apply to a novel signal recovery

In this work, we investigate the strong convergence of the sequences generated by the shrinking projection method and the parallel monotone hybrid method to find a common fixed point of a finite family of $\mathcal{G}$-nonexpansive mappings under suitable conditions in Hilbert spaces endowed with graphs. We also give some numerical examples and provide application to signal recovery under situation without knowing the type of noises. Moreover, numerical experiments of our algorithms which are defined by different types of blurred matrices and noises on the algorithm to show the efficiency and the implementation for LASSO problem in signal recovery.