Optical Processing in Radon Space.
Abstract
The Radon transform is the mathematical basis of computed tomography. The two-dimensional (2D) Radon transform consists of a series of 1D projections of a 2D function, obtained by integrating the function along lines, while the 3D Radon transform consists of 1D projections of a 3D function, obtained by integrating over planes. In both cases, the transform serves to reduce the dimensionality of a function from 2D or 3D to 1D. For signal-processing applications, this dimensionality reduction is very useful because of the availability of sophisticated processing devices, such as SAW and CCD filters, for 1D time signals. The Radon transform permits the use of these devices with 2D and 3D data sets. The operations that can be performed with the help of the Radon transform include: convolution, correlation, Fourier analysis, bandwidth compression, space-variant filtering, adaptive filtering, calculation of the Wigner distribution and ambiguity function, and calculation of moments of an image. In all of these cases, the operations can be carried out on a 2D or 3D data set by first performing a Radon transform, then doing a sequence of 1D operations, and finally performing an inverse Radon transform.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1983
- Accession Number
- ADA137033
Entities
People
- H. H. Barrett
Organizations
- University of Arizona