Iteratively solving linear inverse problems under general convex constraints. (English) Zbl 1123.65044

Daubechies, Ingrid; Teschke, Gerd; Vese, Luminita

Inverse Probl. Imaging 1, No. 1, 29-46 (2007).

Let \(T\) be a bounded operator from a Hilbert space \({\mathcal H}\) into itself, with \(\| T \|<1\), and \(C\) a closed convex subset of \({\mathcal H}\). For solving linear operator equations \(Tf=h\) the iterative process \(f_{n+1}=(\text{Id}-P_{\alpha C})(f_n+T^*g-T^* T f_n)\), \(\alpha>0\) is proposed. The cases of bounded and unbounded \((T^* T)^{-1}\) are considered.

Reviewer: Mikhail Yu. Kokurin (Yoshkar-Ola)

MSC:

65J10	Numerical solutions to equations with linear operators (do not use 65Fxx)
65J22	Numerical solution to inverse problems in abstract spaces
47A50	Equations and inequalities involving linear operators, with vector unknowns

Keywords:

linear inverse problems; Landweber iteration; Besov- and BV restoration; generalized shrinkage; Hilbert space; linear operator equations