Image reconstruction from finite numbers of projections

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Abstract
Several results are obtained appertaining to the reconstruction of a two- dimensional image from a finite number of projections. Several schemes are considered for interpolating between the given data. When a trigonometrical Fourier series is used for angular interpolation then one finds, firstly, a consistency condition whereby a posteriori estimates can be made of the errors in the given data, and secondly, a basic image which contains only that information common to all physically permissible interpolation schemes. This basic image is necessarily free of misleading artefacts but it is computationally slow. Several computationally rapid interpolation schemes (based on the fast Fourier transform algorithm) are found to give good quality images, provided the given number of projections is sufficient to resolve the major details of the true image. A computational example is presented showing that a contrived image can be accurately reconstructed from a single projection.