On Wiener type filtrations in the single-photon emission computed tomography

Jean-Pol Guillement (1) , Roman Novikov (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

For 2D data with Poisson noise we give explicit formulas for the optimal space-invariant Wiener type filter with some a priori geometric restrictions on the window function. Proceeding from this result we (1) explain (in particular) an efficiency of some well-known "1D" (approximately optimal) space-invariant Wiener type filtering scheme (with unknown object power spectrum) in single-photon emission computed tomography (SPECT) and positron emission tomography (PET) imaging based on the classical FBP algorithm (or its iterative use) and (2) propose also an efficient 2D ( approximately optimal) space-invariant Wiener type filtration (with unknown object power spectrum) for SPECT imaging based on the generalized FBP algorithm (implementing the explicit formula for the nonuniform attenuation correction) and/or the classical FBP algorithm (used iteratively). An efficient space-variant version of the latter 2D filtration is also announced. Numerical examples illustrating the aforementioned results (in the framework of simulated SPECT imaging) are given.

Mots clés: Wiener filters; SPECT; PET

Domaines: Analyse numérique [math.NA]

Jean-Pol Guillement, Roman Novikov. On Wiener type filtrations in the single-photon emission computed tomography. 2007. ⟨hal-00150503v1⟩