Image Reconstruction From Projections Using Circular Harmonic Expansion

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Abstract
A method is described for image reconstruction which processes the projection data in polar rather than rectangular coordinates, and does not require backprojection. It is based on the decomposition of the object and its shadow (set of projections) into "circular harmonics," or radial modulators of angular Fourier components. An inverse filter is derived which enables the radial modulators of the object to be reconstructed from those of the shadow. Experimental results from digital and coherent optical implementations are given. A real time optical reconstruction processor is proposed.

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