Image Reconstruction from Truncated Data in Single-Photon Emission Computed Tomomgraphy with Uniform Attenuation

Frederic Noo (1) , Michel Defrise (2) , Jed Pack (3) , Rolf Clackdoyle (4)

1 UCAIR - Utah Center for Advanced Imaging Research [Salt Lake City]
2 Department of Nuclear Medicine
3 CT Systems and Applications Lab
4 LHC - Laboratoire Hubert Curien

We present a mathematical analysis of the problem of image reconstruction from truncated data in two-dimensional (2D) single-photon emission computed tomography (SPECT). Recent results in classical tomography have shown that accurate reconstruction of some parts of the object is possible in the presence of truncation. We have investigated how these results extend to 2D parallel-beam SPECT, assuming that the attenuation map is known and constant in a convex region $\Omega$ that includes all activity sources. Our main result is a proof that, just like in classical tomography accurate SPECT reconstruction at a given location x ∈ $\Omega$,does not require the data on all lines passing through $\Omega$; some amount of truncation can be tolerated. Experimental reconstruction results based on computer-simulated data are given in support of the theory.

Domaines: Analyse fonctionnelle [math.FA]; Imagerie médicale

Frederic Noo, Michel Defrise, Jed Pack, Rolf Clackdoyle. Image Reconstruction from Truncated Data in Single-Photon Emission Computed Tomomgraphy with Uniform Attenuation. Inverse Problems, 2007, pp.645-667. ⟨10.1088/0266-5611/23/2/011⟩. ⟨ujm-00137068⟩