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27 September 2011 Some proximal methods for CBCT and PET tomography
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Abstract
The reconstruction of the images obtained via the Cone Beam Computerized Tomography (CBCT) and Positron Emission Tomography (PET) Scanners are ill-posed inverse problems. One needs to adress carefully the problem of inversion of the mathematical operators involved. Recent advances in optimization have yielded efficient algorithms to solve very general classes of inverse problems via the minimization of non-differentiable convex functions. We show that such models are well suited to solve the CBCT and PET reconstruction problems. On the one hand, they can incorporate directly the physics of new acquisition devices, free of dark noise; on the other hand, they can take into account the specificity of the pure Poisson noise. We propose various fast numerical schemes to recover the original data and compare them to state-of-the-art algorithms on simulated data. We study more specifically how different contrasts and resolutions may be resolved as the level of noise and/or the number of projections of the acquired sinograms decrease. We conclude that the proposed algorithms compare favorably with respect to well-established methods in tomography.
© (2011) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
S. Anthoine, J. F. Aujol, Y. Boursier, and C. Melot "Some proximal methods for CBCT and PET tomography", Proc. SPIE 8138, Wavelets and Sparsity XIV, 81381E (27 September 2011); https://doi.org/10.1117/12.893415
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