Image representation and compression with the fractional Fourier transform

Abstract

We discuss the application of fractional Fourier transform-based ®ltering con®gurations to image representation and compression. An image can be approximately represented (and stored or transmitted) as the coe cients of the minimum mean square ®ltering con®guration approximating the image matrix. An order of magnitude compression is possible with moderate errors with the raw method. While inferior to commonly available compression algorithms, the results presented correspond to the basic method without any re®nement or combination with other techniques, suggesting that the approach may hold promise for future development. Regardless of its practical usefulness, the fact that the information inherent in an image can be decomposed or factored into fractional Fourier domains is of considerable conceptual signi®cance. The information contained in the image is distributed to the di erent domains in an unequal way, making some domains more dispensible than others in representing the image. Ó 2001 Published by Elsevier Science B.V.

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