Yves Goussard – Optimization Online

Metal Artefact Reduction by Least-Squares Penalized-Likelihood Reconstruction with a Fast Polychromatic Projection Model

Published: 2009/12/14

Biomedical Applications, Bound-constrained Optimization beam hardening, computed tomography, metal artifacts, nonlinear optimization, polychromatic projection, runtime reduction

We consider penalized-likelihood reconstruction for X-ray computed tomography of objects that contain small metal structures. To reduce the beam hardening artefacts induced by these structures, we derive the reconstruction algorithm from a projection model that takes into account the photon emission spectrum and nonlinear variation of attenuation to photon energy. This algorithm requires excessively long … Read more

On the Stopping Criterion for Numerical Methods Used to Solve Linear Systems with Additive Gaussian Noise

Published: 2009/09/21, Updated: 2009/12/04

Jean-Pierre Dussault

Yves Goussard

Benoit Hamelin

Statistics, Unconstrained Optimization gibbs prior, least squares, map, regularization, stopping condition

We consider the inversion of a linear operator with centered Gaussian white noise by MAP estimation with a Gaussian prior distribution on the solution. The actual estimator is computed approximately by a numerical method. We propose a relation between the stationarity measure of this approximate solution to the mean square error of the exact solution. … Read more