Quantitative image recovery theorems

This paper provides a quantitative version of the classical image recovery problem to find an ϵϵ-approximate solution of the problem. The rate of asymptotic regularity of the iteration schemas, connected with the problem of image recovery, coincides with the existing optimal and quadratic bound for Krasnoselskii–Mann iterations. We then provide explicit effective and uniform bounds on the approximate fixed points of the mappings under consideration to be an approximate solution of the image recovery problem up to a uniform change from ϵϵ to δ(ϵ)δ(ϵ). When combined, these results provide algorithms with explicit rates of convergence for the recovery of an ϵϵ-perturbation of the original image in different settings.