Symmetric Convolution. Using Unitary Transform Matrices: A New Approach to Image Reconstruction
Abstract
The Air Force images space-borne objects from the ground with optical systems that suffer from the effects of atmospheric turbulence. Many image processing techniques exist to alleviate these effects, but they are computationally complex and require large amounts of processing time. A faster image processing system would greatly improve images of objects observed through the turbulent atmosphere and help national strategists glean higher quality intelligence on other nations space platforms. One promising mathematical method to decrease the computational complexity of image processing algorithms involves symmetric convolution. Symmetric convolution is a recently discovered property of trigonometric transforms that allows the convolution of sequences to be calculated through point multiplication in the trigonometric transform domain. This method holds distinct advantages over existing matrix techniques. The versions of the transform matrices for symmetric convolution are similar but not exactly equal to standard unitary versions of trigonometric transforms. This paper demonstrates relationships between the two types of transform matrices, and then uses the new relationships to derive forms of the symmetric convolution-multiplication property based on unitary rather than convolutional forms of the transform matrices. It further describes how image processing algorithms based on unitary transforms can be included in future-generation optical surveillance systems.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1999
- Accession Number
- ADA396545
Entities
People
- Thomas M. Foltz
Organizations
- Air Command and Staff College