Orthogonal discrete periodic Radon transform. Part II: Applications

In this paper, we study the properties and possible applications of the newly proposed orthogonal discrete periodic Radon transform (ODPRT). Similar to its previous version, the new ODPRT also possesses the useful properties such as the discrete Fourier slice theorem and the circular convolution property. They enable us to convert a 2-D application into some 1-D ones such that the computational complexity is greatly reduced. Two examples of using ODPRT in the realization of 2-D circular convolution and blind image resolution are illustrated. With the fast ODPRT algorithm, efficient realization of 2-D circular convolution is achieved. For the realization of blind image restoration, we convert the 2-D problem into some 1-D ones that reduces the computation time and memory requirement. Besides, ODPRT adds more constraints to the restoration problem in the transform domain that makes the restoration solution better. Significant improvement is obtained in each case when comparing with the traditional approaches in terms of quality and computation complexity. They illustrate the potentially widespread applications of the proposed technique.