Reducing the Cost of Removing Border Artefacts in Fourier Transforms

Many image processing algorithms are implemented in a combination of spatial and frequency domains. The fast Fourier transform (FFT) is the workhorse of such algorithms. One limitation of the FFT is artefacts that result from the implicit periodicity within the spatial domain. A new periodic plus smooth decomposition has recently been proposed for removing such artefacts, although this comes at the cost of an additional 2D FFT. In this paper, we restructure the decomposition to enable it to be calculated with a single 1D FFT, which can significantly accelerate artefact free Fourier transformation. The cost of this acceleration is a small amount of additional storage to hold the representation of the smooth image component.

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