Abstract: We gave an adaptive  regularization method  for solving monotonic variational inclusion problems in  Hilbert space. Firstly, we used adaptive rules to eliminate the dependence of iterative step-sizes on operators in the convergence analysis of existing algorithms. Secondly, we combined regularization technique to establish strong convergence theorems for solving variational inclusion problems. Finally,  the convergence and superiority of the  proposed algorithm were demonstrated through image reconstruction experiment.

Key words: variational inclusion problem, adaptive algorithm, regularization, strong convergence, image reconstruction