An explicit closed-form solution to the limited-angle discrete tomography problem for finite-support objects

We present an explicit formula for reconstructing a finite-support object defined on a lattice of points and taking on integer values from a finite number of its discrete projections over a limited range of angles. We make extensive use of the discrete Fourier transform in doing so. Our approach computes the object sample values directly as a linear combination of the projections sample values. The well-known ill-posedness of the limited angle tomography problem manifests itself in some very large coefficients in these linear combinations; these coefficients (which are computed off-line) provide a direct sensitivity measure of the reconstruction samples to the projections samples. The discrete nature of the problem implies that the projections must also take on integer values; this means noise can be rejected. This makes the formula practical.