SMOOTHEST-MODEL RECONSTRUCTION FROM PROJECTIONS

A new algorithm, based on Tikhonov regularization with a differential operator, is proposed for image reconstruction from projection data. T he algorithm reconstructs the smoothest image amongst all possible ima ges yielding a given fit to the data. In addition, the algorithm compu tes measures of the spatial resolution and variance of the constructed image, which characterize its non-uniqueness due to incomplete data c overage and noise in the data. Under the assumption of straight raypat hs and a circular imaging region, we derive analytical expressions for the reconstructed image and resolution/variance measures. For a fixed data acquisition geometry and fixed noise statistics, the reconstruct ion is linear in the data and the non-uniqueness measures are independ ent of the data, suggesting the possibility of applying a precomputed inversion operator to new data sets to achieve real-time image constru ction. Numerical examples show that the new technique works at least a s well as the algebraic reconstruction technique (ART) and is stable a gainst strong noise in the data.