Combining Image Reconstruction and Image Analysis with an Application to Two-Dimensional Tomography

The tasks of image reconstruction from measured data and the analysis of the resulting images are more or less strictly separated. One group of scientists computes by applying reconstruction algorithms to the images; the other then operates on these images to enhance the analysis. First attempts at combining image reconstruction and image analysis, in a nonsystematic 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., even 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 a 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.