title: Regularization in tomographic reconstruction using thresholding estimators.
abstract: In tomographic medical devices such as single photon emission computed tomography or positron emission tomography cameras, image reconstruction is an unstable inverse problem, due to the presence of additive noise. A new family of regularization methods for reconstruction, based on a thresholding procedure in wavelet and wavelet packet (WP) decompositions, is studied. This approach is based on the fact that the decompositions provide a near-diagonalization of the inverse Radon transform and of prior information in medical images. A WP decomposition is adaptively chosen for the specific image to be restored. Corresponding algorithms have been developed for both two-dimensional and full three-dimensional reconstruction. These procedures are fast, noniterative, and flexible. Numerical results suggest that they outperform filtered back-projection and iterative procedures such as ordered-subset-expectation-maximization.
authors.affiliation: Department of Biomedical Engineering, Columbia University, New York, NY 10027, USA.
authors.forename: Jérôme
authors.initials: J
authors.lastname: Kalifa
authors.forename: Andrew
authors.initials: A
authors.lastname: Laine
authors.forename: Peter D
authors.initials: PD
authors.lastname: Esser
mesh_terms: D000465:Algorithms; D001842:Bone and Bones / Q000000981:diagnostic imaging; D001921:Brain / Q000000981:diagnostic imaging; D006801:Humans; D007090:Image Interpretation, Computer-Assisted / Q000295:instrumentation / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D019047:Phantoms, Imaging; D012815:Signal Processing, Computer-Assisted; D014054:Tomography / Q000379:methods; D014055:Tomography, Emission-Computed / Q000379:methods*; D015899:Tomography, Emission-Computed, Single-Photon / Q000379:methods