Publications [#287181] of Ingrid Daubechies

Papers Published

1. Daubechies, I; Teschke, G; Vese, L, On some iterative concepts for image restoration, Advances in Imaging and Electron Physics, vol. 150 (January, 2008), pp. 1-51, Elsevier, ISSN 1076-5670 [doi]
   (last updated on 2025/04/04)

   Abstract:
   Several iterative strategies for solving inverse problems in the context of signal and image processing are discussed. Problems for which it is reasonable to assume that the solution has a sparse expansion with respect to a wavelet basis or frame are focused. A variational formulation of the problem is considered and an iteration scheme for which the iterates approximate the solution is constructed. The concrete problem of simultaneously denoising, decomposing, and deblurring a given image, is discussed. The associated variational formulation of the problem contains terms that promote sparsity and smoothness. A natural extension to vector-valued inverse problems is also considered. In the linear case, and under fairly general assumptions on the constraint, its is proved that weak convergence of the iterative scheme always holds.