Reconstructing Interior Head Tissue from X-ray Transmissions

over certain thin strips L in the plane are measured through x-ray transmission along L. How can we recover f(x,y)? Previous reconstruction algorithms fall into two broad categories: (a) Algorithms based on a formula, typically the Fourier inversion formula.lvE (b) Search algorithms, typically based on iterative relaxation.2,4 We have chosen a particular f(x,y), Fig. 1, felt to be a reasonable model of a section of the skull and have computed Pf(L) directly. We then compared the reconstructions of f by the various algorithms, Figs. 2-6. While all algorithms studied successfully reconstruct the position of the (denser) skull itself, interior tissue (which varies by only a few percent) was reconstructed very accurately by an algorithm of type (a), which is a modification of an algorithm proposed by Ramachandran and Lakshminarayanan.6 The best one of type (b) we could find failed to reconstruct the interior tissues. 2a. Fourier Algorithms The basis of Fourier algorithms is that if P(t,O) denotes the integral of f along the line L(t,0), i.e.