We present a new approach to convergence rate results for variational regularization. Avoiding Bregman distances and using image space approximation rates as source conditions we prove a nearly minimax theorem showing that the modulus of continuity is an upper bound on the reconstruction error up to a constant. Applied to Besov space regularization we obtain convergence rate results 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 source conditions, bounds on the defect of the Tikhonov functional, and image space approximation rates.

翻译：我们为变异性正规化提出了一种新的趋同率结果方法。 避免布雷格曼距离和使用图像空间近似率作为源条件,我们证明了一种近乎微小的理论,表明连续性模范是重建错误的上限,直到一个常数。 应用到贝索夫空间正规化,我们获得了0. 2,q美元和0. p, p 美元-罚款的趋同率结果,没有限制$p, q@in (1, infty) 。 最后,我们证明了H\"老式变异源条件的等值,与Tikhonov功能缺陷和图像空间近似率的等值。