Smoothest-model reconstruction from projections

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Abstract
A new algorithm, based on Tikhonov regularization with a differential operator, is proposed for image reconstruction from projection data. The algorithm reconstructs the smoothest image amongst all possible images yielding a given fit to the data. In addition, the algorithm computes measures of the spatial resolution and variance of the constructed image, which characterize its non-uniqueness due to incomplete data coverage and noise in the data. Under the assumption of straight raypaths and a circular imaging region, the authors derive analytical expressions for the reconstructed image and resolution/variance measures. For a fixed data acquisition geometry and fixed noise statistics, the reconstruction is linear in the data and the non-uniqueness measures are independent of the data, suggesting the possibility of applying a precomputed inversion operator to new data sets to achieve real-time image construction. Numerical examples show that the new technique works at least as well as the algebraic reconstruction technique (ART) and is stable against strong noise in the data.

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