In this paper, we have proposed a new fully parallel splitting method for the stable principal component pursuit problem, which inherits all merits of ADMM and parallel method.
Yin, "Parallel multi-block ADMM with o(1/k) convergence," Journal of Scientific Computing, vol.
Yuan, "The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent," Mathematical Programming, vol.
For the latter case, we mention that in  an EM algorithm along with a smooth approximation of [[parallel][nabla]u[parallel].sub.1] was proposed to solve the Poisson-TV problem; in  a multiplicative gradient based algorithm (equivalent to the penalized EM algorithm) was used; a multilevel algorithm was used in  to solve a modified version of (43); in  the authors used the [l.sup.1] regularized loss minimization (a particular case of the ADMM algorithm, see [61, Section 6.3]) to minimize (43); in  two alternative variational methods were used (called L2-L2Log and TV-log) which can be understood as a change of variable ([z.sup.k] = log([(Au).sub.k])) in (43).
is not the only alternative within the TV framework to restore images corrupted with Speckle noise; here we mention that  (the first method within the TV framework), used a constrained optimization approach with two Lagrange multipliers; the denoising and deconvolution problems were addressed; additionally in  the multiplicative model was converted into an additive one and used a multigrid algorithm to solve the resulting Euler-Lagrange equation; Also in  the multiplicative model was converted into an additive one and used the SB (or ADMM) algorithm to solve the optimization problem; only the denoising problem was addressed.