Adel Faridani

A generalized sampling theorem for locally compact abelian groups

We present a sampling theorem for locally compact abelian groups. The sampling sets are finite unions of cosets of a closed subgroup. This generalizes the well-known case of non-equidistant but periodic sampling on the real line. For non-bandlimited functions an L1-type estimate for the aliasing error is given. We discuss the application of the theorem to a class of sampling sets in R s ; give a general algorithm for computer implementation; present a detailed description of the implementation for the s-dimensional torus group; and point out connections to lattice rules for numerical integration.

Examples of local tomography

This note is a reorganization of the examples in [Faridani, Ritman, and Smith, SIAM J. Appl. Math., 52(1992), pp. 459–484], which became disorganized while the article was in press.

High-resolution computed tomography from efficient sampling

This paper investigates high-resolution reconstructions from efficiently sampled data in parallel-beam tomography, in particular, local tomography. A class of sampling schemes is defined and characterized, and it is shown that the standard scheme and the interlaced scheme of Cormack (Cormack A M 1978 Phys. Med. Biol. 23 1141-8) are most promising. An error analysis for the filtered backprojection algorithm for both global and local tomography is presented. The analysis provides insights on how to realize the theoretically superior resolution of the interlaced scheme in practice. A numerical experiment with real data indicates the feasibility of high-resolution local tomography using the interlaced scheme.

Local Reconstruction Applied to X-Ray Microtomography

A characteristic of local reconstruction is that the x-ray detector array need only be slightly larger than the projected volume of interest within the object scanned. This feature of local reconstruction has several practical consequences for to- mographic imaging. We present an example in which local reconstruction extends the capability of a micro-CT scanner beyond the limits set by those physical characteristics of the scanner components that would be needed if standard global tomographic reconstruction algorithms were to be used.

Results, Old and New, in Computed Tomography

Computed tomography (CT) entails the reconstruction of a function f from line integrals of f. This mathematical problem is encountered in a growing number of diverse settings in medicine, science, and technology, ranging from the famous application in diagnostic radiology to recent research in quantum optics. As a consequence, many aspects of CT have been extensively studied and are now well understood, thus providing an interesting model case for the study of other inverse problems. Other aspects, notably three-dimensional reconstructions, still provide numerous open problems.

Regions of Backprojection and Comet Tail Artifacts for

We explore two characteristic features of x-ray computed tomography inversion formulas in two and three dimensions that are dependent on

\pi

\pi

-Line Reconstruction Formulas in Tomography

-lines. In such formulas the data from a given source position contribute only to the reconstruction of

Numerical and theoretical explorations in helical and fan-beam tomography

f(\mathbf{x})

Sampling in Parallel-Beam Tomography

for