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We present a new approach to convergence rate results for variationalregularization. Avoiding Bregman distances and using image space approximationrates as source conditions we prove a nearly minimax theorem showing that themodulus of continuity is an upper bound on the reconstruction error up to aconstant. Applied to Besov space regularization we obtain convergence rateresults for $0,2,q$- and $0,p,p$-penalties without restrictions on $p,q\in(1,\infty).$ Finally we prove equivalence of H\"older-type variational sourceconditions, bounds on the defect of the Tikhonov functional, and image spaceapproximation rates.

Variational Regularization Theory Based on Image Space Approximation Rates