The discrete diffraction transform

I. Sedelnikov, Amir Averbuch*, Y. Shkolnisky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper, we define a discrete analogue of the continuous diffracted projection. We define the discrete diffraction transform (DDT) as a collection of the discrete diffracted projections (DDPs) taken at specific set of angles along specific set of lines. The 'DDP' is defined to be a discrete transform that is similar in its properties to the continuous diffracted projection. We prove that when the DDT is applied to a set of samples of a continuous object, it approximates a set of continuous vertical diffracted projections of a horizontally sheared object and a set of continuous horizontal diffracted projections of a vertically sheared object. A similar statement, where diffracted projections are replaced by the X-ray projections, that holds for the 2D discrete Radon transform (DRT), is also proved. We prove that the DDT is rapidly computable and invertible.

Original languageEnglish
Pages (from-to)496-538
Number of pages43
JournalIMA Journal of Applied Mathematics
Issue number3
StatePublished - Jun 2008


  • Diffraction tomography
  • Discrete diffraction transform
  • Radon transform


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