Viscosity modification with parallel inertial two steps forward-backward splitting methods for inclusion problems applied to signal recovery - Cholamjiak, Watcharaporn; Dutta, Hemen (Chaos, solitons and fractals, 2022)
•We investigate the common variational inclusion problem (CVIP) and offer a new parallel technique that combines viscosity modification with parallel inertial two-step forward-backward splitting approaches.•We prove the strongly convergent theorems in Hilbert spaces under some reasonable conditions.•For signal recovery problems requiring several filters, an extensive numerical examination is presented, with comparisons to the inertial parallel monotone hybrid method.•All of the numerical results show that the proposed algorithm solves the signal recovery problem and improves the quality of the observed signal significantly. In this paper, we introduce a new parallel algorithm by combining viscosity modification with parallel inertial two steps forward-backward splitting methods for approximating a solution of common inclusion problems. The strongly convergent theorems are established under some suitable conditions in Hilbert spaces. The applicability and advantages of the new parallel algorithm are presented by using to solve signal recovering problem in compressed sensing. The efficiency of the algorithm is shown by comparing it with some previous parallel algorithms.