论文标题
基于图像空间近似速率的变分正规化理论
Variational Regularization Theory Based on Image Space Approximation Rates
论文作者
论文摘要
我们提出了一种新方法来进行变分正规化的结果。避免Bregman距离并使用图像空间近似速率作为源条件，我们证明了一个几乎最小的定理表明，连续性模量是重建误差上的上限，直至常数。 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 Hölder-type variational source conditions, bounds on the defect of the Tikhonov functional, and image space approximation rates.
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 Hölder-type variational source conditions, bounds on the defect of the Tikhonov functional, and image space approximation rates.
