This paper proposes a new algorithm, the direct cosine method (DCM), to reconstruct the tomogram. This method uses the cosine transform in a similar form as the Fourier transform, in direct Fourier method (DFM). The cosine projection-slice (CPS) theorem needed in the DCM is also derived. The CPS theorem states that the summation of the cosine transform of two projections is a slice of the cosine transform of the projected object. The real computation and good energy compaction will reduce the processing time and errors from truncation and interpolation. By applying the DCM to the reconstruction tomogram, more advanced applications are possible.
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