Constraining by a family of strictly nonexpansive idempotent functions with applications in image reconstruction
When solving an image reconstruction problem a previous knowledge concerning the original image may lead to various constraining strategies. Aconvergence result has been previously proved for a constrained version of the Kaczmarz projection algorithm with a single strictly nonexpansive idempotent function with a closed image. In this paper we consider a more general projection based iterative method and a family of such constraining functions with some additional hypotheses in order to better use the apriori information for every approximation calculated. We present a particular family of box-constraining functions which satisfies our assumptions and we design an adaptive algorithm that uses an iteration-dependent family of constraining functions for some numerical experiments of image reconstruction on Tomographic Particle Image Velocimetry.
image reconstruction constraining strategy projection algorithm strictly nonexpansive functions least squares problems 65f10 65f20 65f22