| 摘要 |
A fast method for divergent-beam backprojecion is proposed for generating an electronic image from a preprocessed divergent-beam sonogram, the sinogram being a collection of divergent beam projections. The method can include the following steps: subdividing the sinogram into multiple sub-sinograms; performing a weighted backprojection of said sub-sinograms, to produce multiple corresponding sub-images; and aggregating said sub-images to create the electronic image. The subdivision of the sinogram into sub-sinograms can be performed in a recursive manner. A dual of the proposed method provides a fast means for reprojecting an electronic image, i.e., generating a divergent-beam sinogram from the image. These methods are applicable to fan-beam and cone-beam tomography utilizing a variety of scanning trajectories, including spiral. These methods do not require rebinning, and offer speedups similar to the FFT when compared to conventional backprojection and reprojection algorithms. Substantial computational savings are obtained without perceptible degradation or significant loss of numerical accuracy.
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