Error estimation for Bregman iterations and inverse scale space methods in image restoration

In this paper we consider error estimation for image restoration problems based on generalized Bregman distances. This error estimation technique has been used to derive convergence rates of variational regularization schemes for linear and nonlinear inverse problems by the authors before (cf. [4, 21, 22]), but so far it was not applied to image restoration in a systematic way. Due to the flexibility of the Bregman distances, this approach is particularly attractive for imaging tasks, where often singular energies (nondifferentiable, not strictly convex) are usedto achieve certain tasks such as preservation of edges. Besides the discussion of the variational image restoration schemes, our main goal in this paper is to extend the error estimation approach to iterative regularization schemes (and timecontinuous flows) that have emerged recently as multiscale restoration techniques and could improve some shortcomings of the variational schemes. We derive error estimates between the it...

• Type: Journal
• Year: 2007
• Where: COMPUTING
• Authors: Martin Burger, E. Resmerita, Lin He
• Keywords: Bregman Distance, COMPUTING 2007, Error Estimation, Image Restoration