Combining image reconstruction and image evaluation

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In medical imaging or in non-destructive testing images are produced which serve as basis for diagnostic evaluation. To that end the images, representing density distributions for example, are further processed in order to facilitate the diagnosis. The two tasks, namely reconstruction of the images from the measured data and enhancement of the reconstructed image are typically performed by different groups, and the applied methods are chosen independently of each other. The idea of the proposal is to merge image reconstruction and image enhancement into just one stable, fast and effiicient algorithm. For the combination of image reconstruction from Radon data and computing partial derivatives this is already published by the applicant, where one reconstruction kernel is derived resulting directly in the derivatives of the image. There are presently only a few methods which combine these two steps, a first systematic attempt was recently published by the applicant. The goal of the proposal is to provide a unified framework for developing reconstruction algorithms for linear functionals of the images, like calculating directly derivatives, calculating smoothed images by linear diffusion or by calculating features of the image like wavelet coefficients. The aspects of regularizing inverse problems, order of convergence and first of all deriving fast and stable algorithms are in the centre of interest.