A variational method for Abel inversion tomography with mixed Poisson-Laplace-Gaussian noise

<p style='text-indent:20px;'>Abel inversion tomography plays an important role in dynamic experiments, while most known studies are started with a single Gaussian assumption. This paper proposes mixed Poisson-Laplace-Gaussian distribution to characterize the noise charge-coupled-device (CCD) sensed radiographic data, and develops multi-convex optimization model address reconstruction problem. The proposed is derived by incorporating varying amplitude approximation expectation maximization algorithm into infimal convolution process. To solve it numerically, variable splitting augmented Lagrangian method integrated block coordinate descent framework, which anisotropic diffusion additive operator employed gain edge preserving computation efficiency. Supplementarily, space of functions adaptive bounded Hessian introduced prove existence uniqueness solution higher-order regularized, quadratic subproblem. Moreover, simplified higher order regularizer for Poisson removal. illustrate performance algorithms, numerical tests on synthesized real digital data performed.</p>