Discussions are made on the minimum angle range for projection data necessary to reconstruct the complete CT image. As is easily shown from the image reconstruction theorem, the lack of projection angle provides no data for the Fourier transformed function of the object on the corresponding angular directions, where the projections are missing. In a normal situation, the Fourier transformed function of an object image holds an analytic characteristic with respect to two-dimensional orthogonal parameters. This characteristic enables uniquely prolonging the function outside the obtained region employing a sort of analytic continuation with respect to both parameters. In the method reported here, an object pattern, which is confined within a finite range, is shifted to a specified region to have complete orthogonal function expansions without changing the projection angle directions. These orthogonal functions are analytically extended to the missing projection angle range and the whole function is determined. This method does not include any estimation process, whose effectiveness is often seriously jeopardized by the presence of a slight fluctuation component. Computer simulations were carried out to demonstrate the effectiveness of the method.

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