Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Digital Image Restoration
Image Representation Via a Finite Radon Transform
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Signal Processing
The discrete periodic Radon transform
IEEE Transactions on Signal Processing
Image restoration using the W-slice method
IEEE Transactions on Image Processing
Generalized Discrete Radon Transforms and Their Use in the Ridgelet Transform
Journal of Mathematical Imaging and Vision
Orthogonal discrete radon transform over pn × pnimages
Signal Processing - Special section: Advances in signal processing-assisted cross-layer designs
Blind image deblurring driven by nonlinear processing in the edge domain
EURASIP Journal on Applied Signal Processing
International Journal of Communication Networks and Distributed Systems
Reply to "Comments on 'The discrete periodic radon transform'"
IEEE Transactions on Signal Processing
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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.