Orthogonal discrete periodic Radon transform. Part I: theory and realization

The discrete periodic Radon transform (DPRT) was proposed recently. It was shown that DPRT possesses many useful properties that are similar to the conventional continuous Radon transform. Using these properties, a 2-D signal can be processed by some 1-D approaches to reduce the computational complexity. However, the non-orthogonal structure of DPRT projections introduces redundant operations that often lower the efficiency of the technique in applications. In this paper, we propose the orthogonal discrete periodic Radon transform (ODPRT) in which a new decomposition approach is introduced. All ODPRT projections are modified to be orthogonal such that redundancy is eliminated. Furthermore, we consider the efficient realization for computing ODPRT and its inverse that make the proposed ODPRT more feasible in practical applications.

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