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Partitioned Image Filtering for Reduction of the Gibbs Phenomenon

The aim of this paper is to propose a partitioned-image filtering technique that is a new way of reducing the Gibbs phenomenon in filtered images. Methods: This technique relies on exploiting the properties of the Gibbs phenomenon and on assumptions about the structure of the image. The amplitude of the Gibbs ringing is directly proportional to the height of the image discontinuity. If the height of the discontinuity can be reduced, then the subsequent ringing will also be reduced. Separating the image into stratified layers or partitions reduces the height of the discontinuity significantly. Each partition is filtered separately and recombined nonlinearly to yield the final filtered image. This method weakens filtering of image edges that have large discontinuities, thus reducing the Gibbs phenomenon while simultaneously reducing the image noise. Results: The proposed filtering method has been applied to a simple image with only 2 intensity values to illustrate the implementation steps. The method has also been applied to 2 SPECT patient studies to show the effectiveness of the proposed filtering method, which can significantly reduce the Gibbs artifacts. Conclusion: The Gibbs phenomenon in a filtered image can be reduced by partitioning the image so that the amplitude of the discontinuity is controlled. The proposed method is efficient and simple in implementation, with fast Fourier transform.