This dissertation considers a method for processing two-dimensional (2-D) signals (e.g. imagery) by transformation to a coordinate space where the 2-D operation separates into orthogonal 1-D operations. After processing, the 2-D output is reconstructed by a second coordinate transformation. This approach is based on the Radon transform, which maps a two-dimensional Cartesian representation of a signal into a series of one-dimensional signals by line-integral projection. The mathematical principles of this transformation are well-known as the basis for medical computed tomography. This approach can process signals more rapidly than conventional digital processing and more flexibly and precisely than optical techniques. A new formulation of the Radon transform is introduced that employs a new transformation--the central-slice transform--to symmetrize the operations between the Cartesian and Radon representations of the signal and to aid in analyzing operations that may be susceptible to solution in this manner. It is well-known that 2-D Fourier transforms and convolutions can be performed by 1-D operations after Radon transformation, as proven by the central-slice and filter theorems. Demonstrations of these operations via Radon transforms are described. An optical system has been constructed to derive the line-integral projections of 2-D transmissive or reflective input data. Fourier transforms of the projections are derived by a surface-acoustic-wave chirp Fourier transformer, and filtering is performed in a surface-acoustic-wave convolver. Reconstruction of the processed 2-D signal is performed optically. The system can process 2-D imagery at approximately 5 frames/second, though rates to 30 frames/second are achievable if a faster image rotator is added. Other signal processing operations in Radon space are demonstrated, including Labeyrie stellar speckle interferometry, the Hartley transform, and the joint coordinate-frequency representations such as the Wigner distribution function. Other operations worthy of further study include derivation of the 2-D cepstrum, and several spectrum estimation algorithms.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/183978 |
| Date | January 1986 |
| Creators | EASTON, ROGER LEE, JR. |
| Contributors | Barrett, Harrison H. |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | English |
| Detected Language | English |
| Type | text, Dissertation-Reproduction (electronic) |
| Rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. |
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