  This paper derives two new optimization-driven Monte Carlo algorithms
inspired from variable splitting and data augmentation. In particular, the
formulation of one of the proposed approaches is closely related to the
alternating direction method of multipliers (ADMM) main steps. The proposed
framework enables to derive faster and more efficient sampling schemes than the
current state-of-the-art methods and can embed the latter. By sampling
efficiently the parameter to infer as well as the hyperparameters of the
problem, the generated samples can be used to approximate Bayesian estimators
of the parameters to infer. Additionally, the proposed approach brings
confidence intervals at a low cost contrary to optimization methods.
Simulations on two often-studied signal processing problems illustrate the
performance of the two proposed samplers. All results are compared to those
obtained by recent state-of-the-art optimization and MCMC algorithms used to
solve these problems.
