A Constrained Gauss-Newton Algorithm for Material Decomposition in Spectral Computed Tomography
Résumé
Spectral computed tomography exploits energy-resolved detectors to recover the material composition of an object. Material decomposition is a challenging nonlinear and ill-posed inverse problem. While regularization improves the decomposition , the resulting material maps do not satisfy physical constraints (e.g., positivity). In this work, we propose a fast second-order algorithm for constrained material decomposition. The proposed constrained Gauss-Newton algorithm is compared to a standard (unconstrained) Gauss-Newton algorithm on two realistic numerical phantoms. An improved decomposition is obtained for both phantoms. We also found that the constraints must be enforced progressively during the iterations.
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