Regularisation of the limited data computed tomography problem via the boundary element method

We present a new variational approach to the problem of computed tomography reconstruction from sparse data. We use a Tikhonov regularisation (quite different from that of Louis [1985]) which deals without approximation with discrete or nonuniform grids. Our algorithm requires calculation of a Green's function on a finite region and we show how this can be done very efficiently computationally using the numerical/analytic boundary element method (BEM).