Andrew Markoe

Fourier Inversion of the Attenuated X-Ray Transform

A variably attenuated x-ray transform is shown to be invertible via an integral formula for the inversion of the exponential x-ray transform.The attenuation must be known and constant in a convex set containing the unknown emitter. However the attenuation can be otherwise arbitrary.If

An Elementary Proof of Local Invertibility for Generalized and Attenuated Radon Transforms

\mu

Analytic families of differential complexes

denotes the attenuation constant of the exponential x-ray transform then the integral formula computes the Fourier transform of the emitter on all of

Runge families and increasing unions of Stein spaces

R^n

New equations for density, entropy, heat capacity, and potential temperature of a saline thermal fluid

from the values of the Fourier transform on the set

Runge families and inductive limits of Stein spaces

A^\mu = \{ {\sigma + i\mu \omega \in C^n |\omega \in S^{n - 1} ,\sigma \bot \omega } \}

A CHARACTERIZATION OF NORMAL ANALYTIC SPACES BY THE HOMOLOGICAL CODIMENSION OF THE STRUCTURE SHEAF

. Of course F. Natterer [Numer. Math., 32 (1979), pp. 431–438] showed that the values of the Fourier transform of the emitter can be obtained from the Fourier transform of the exponential x-ray transform. In essence however the basic method is analytic continuation from the set

Families of strongly pseudoconvex manifolds

A^\mu

Invariance of holomorphic convexity under proper mappings

.A consequence of the integral formula is a uniqueness theorem for attenuated x-ray transforms of the type considered here: if the transforms ...

Cohomology of analytic families of differential complexes

There is a great deal of current interest in inverting attenuated Radon transforms which occur in single photon emission tomography. These transforms are special cases of generalized Radon transforms