Symmetric Convolution Using Unitary Transform Matrices

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.

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