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In this paper we will present two methods for the reronstruction of a two-dimensional picture from its one-dimensional projections at various angles. The first method is recursive, and the second is nonrecursive. Both of these methods have potential applications in picture transmission, and offer valuable insight into the more general problem of reconstruction of three-dimensional objects from their two-dimensional projections. We will illustrate the numerical details of each method by considering the reconstruction of a picture discretized on a 32 X 32 grid, and compare their relative merits. These two methods will also be compared with other methods suggested in the literature.