Combining Image Reconstruction and Image Analysis with an Application to 2d – Tomography

The tasks of image reconstruction from measured data and the analysis of the so produced images are more or less strictly separated. One group computes by applying reconstruction algorithms the images, the other starts out of that by operating on these images to enhance the analysis. First attempts, in a non systematic way, are known, as Lambda tomography or Tikhonov Phillips methods with `1 – norms or with level – set methods. The aim of this paper is to provide a general tool to combine these two steps; i.e., already in the reconstruction step the future image analysis step is taken into account leading to a new reconstruction kernel. Here we concentrate on linear methods. As practical example we consider the image reconstruction problem in computerized tomography followed by an edge detection. We calculate a new reconstruction kernel and present results from simulations.