Orthogonal discrete Radon transform over pⁿ × pⁿ images

This paper presents a discrete Radon transform based on arrays of size pⁿ × pⁿ where p is prime ( p {greater than or slanted equal to} 2 ) and n ∈ N. The finite Radon transform presented in [F. Matus, J. Flusser, Image representation via a finite Radon transform, IEEE Trans. Pattern Anal. Mach. Intell. 15 (10) (1993) 996-1006] and the discrete periodic Radon transform (DPRT) presented in [T. Hsung, D. Lun, W. Siu, The discrete periodic Radon transform, IEEE Trans. Signal Process. 44 (10) (1996) 2651-2657] are subsets of this more general transform with n restricted to 1 and p restricted to 2, respectively. This transform exactly and invertibly maps the image as pⁿ + p^{n - 1} projections of length pⁿ wrapped under modulo pⁿ arithmetic. Since pⁿ has factors if n > 1, this mapping is partly redundant and a version utilising orthogonal bases is required. An invertible form of the DPRT with orthogonal bases, the orthogonal DPRT (ODPRT), was developed in [D. Lun, T. Hsung, T. Shen, Orthogonal discrete periodic Radon transform. Part I: theory and realization, Signal Processing 83 (5) (2003) 941-955]. An orthogonal version for the generalised pⁿ case is developed here with applications analogous to those of the ODPRT presented in [D. Lun, T. Hsung, T. Shen, Orthogonal discrete periodic Radon transform, Part II: applications, Signal Processing 83 (5) (2003) 957-971].