On the efficiency of proximal methods in CBCT and PET

Cone Beam Computerized Tomography (CBCT) and Positron Emission Tomography (PET) Scans are medical imaging devices that require solving ill-posed inverse problems. The models considered come directly from the physics of the acquisition devices, and take into account the specificity of the (Poisson) noise. We propose various fast numerical schemes to compute the solution. In particular, we show that a new algorithm recently introduced by A. Chambolle and T. Pock is well suited in the PET case when considering non differentiable regularizations such as total variation or wavelet ℓ₁-regularization. Numerical experiments indicate that the proposed algorithms compare favorably with respect to well-established methods in tomography.