Title :
The discrete periodic Radon transform
Author :
Hsung, TaiChiu ; Lun, Daniel P K ; Siu, Wan-chi
Author_Institution :
Hong Kong Polytech. Univ., Hong Kong
fDate :
10/1/1996 12:00:00 AM
Abstract :
In this correspondence, a discrete periodic Radon transform and its inversion are developed. The new discrete periodic Radon transform possesses many properties similar to the continuous Radon transform such as the Fourier slice theorem and the convolution property, etc. With the convolution property, a 2-D circular convolution can be decomposed into 1-D circular convolutions, hence improving the computational efficiency. Based on the proposed discrete periodic Radon transform, we further develop the inversion formula using the discrete Fourier slice theorem. It is interesting to note that the inverse transform is multiplication free. This important characteristic not only enables fast inversion but also eliminates the finite-word-length error that may be generated in performing the multiplications
Keywords :
Fourier transforms; Radon transforms; computational complexity; convolution; image reconstruction; 1D circular convolutions; 2D circular convolution; Fourier slice theorem; computational efficiency; convolution property; discrete periodic Radon transform; finite-word-length error; image reconstruction; inverse transform; inversion; Arithmetic; Character generation; Computational efficiency; Computed tomography; Convolution; Discrete Fourier transforms; Discrete transforms; Fourier transforms; Magnetic resonance imaging; Remote sensing;
Journal_Title :
Signal Processing, IEEE Transactions on