The aim of this paper is twofold. First, several basic mathematical concepts involved in the construction and study of Bregman type iterative algorithms are presented from a unified analytic perspective. Also, some gaps in the current knowledge about those concepts are filled in. Second, we employ existing results on total convexity, sequential consistency, uniform convexity and relative projections in order to define and study the convergence of a new Bregman type iterative method of solving operator equations.

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This paper deals with quantitative aspects of regularization for ill-posed linear equations in Banach spaces, when the regularization is done using a general convex penalty functional. The error estimates shown here by means of Bregman distances yield better convergences rates than those already known for maximum entropy regularization, as well as for total variation regularization.