Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
IMA Journal of Applied Mathematics (2008) 73, 496-538 doi:10.1093/imamat/hxn010
 

Summary: IMA Journal of Applied Mathematics (2008) 73, 496-538
doi:10.1093/imamat/hxn010
Advance Access publication on April 29, 2008
The discrete diffraction transform
I. SEDELNIKOV, A. AVERBUCH AND Y. SHKOLNISKY
School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel
[Received on 8 December 2006; accepted on 4 March 2008]
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.
Keywords: diffraction tomography; discrete diffraction transform; Radon transform.
1. Introduction
Ultrasound imaging is an example of diffracted tomography (see Kak & Slaney, 2001). X-ray tomog-
raphy, mathematically described by the continuous Radon transform, is an example of non-diffracted

  

Source: Averbuch, Amir - School of Computer Science, Tel Aviv University

 

Collections: Computer Technologies and Information Sciences