Regularization in tomographic reconstruction using thresholding estimators

• Published in: IEEE transactions on medical imaging Vol. 22; no. 3; pp. 351 - 359
• Main Authors: Kalifa, J., Laine, A., Esser, P.D.
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.03.2003; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additive noise; Algorithms; Biomedical imaging; Bone and Bones - diagnostic imaging; Brain - diagnostic imaging; Cameras; Humans; Image Interpretation, Computer-Assisted - instrumentation; Image Interpretation, Computer-Assisted - methods; Image reconstruction; Image restoration; Imaging, Three-Dimensional - methods; Inverse problems; Iterative algorithms; Phantoms, Imaging; Positron emission tomography; Signal Processing, Computer-Assisted; Single photon emission computed tomography; Tomography - methods; Tomography, Emission-Computed - methods; Tomography, Emission-Computed, Single-Photon - methods; Wavelet packets
• ISSN: 0278-0062; 1558-254X
• DOI: 10.1109/TMI.2003.809691

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.