A Kullback-Leibler approach for 3D reconstruction of spectral CT data corrupted by Poisson noise

Tom Hohweiller (1) , Nicolas Ducros (1) , Françoise Peyrin (1, 2) , Bruno Sixou (1)

1 Imagerie Tomographique et Radiothérapie
2 ESRF - European Synchrotron Radiation Facility

While standard computed tomography (CT) data do not depend on energy, spectral computed tomography (SPCT) acquire energy-resolved data, which allows material decomposition of the object of interest. Decompo-sitions in the projection domain allow creating projection mass density (PMD) per materials. From decomposed projections, a tomographic reconstruction creates 3D material density volume. The decomposition is made possible by minimizing a cost function. The variational approach is preferred since this is an ill-posed non-linear inverse problem. Moreover, noise plays a critical role when decomposing data. That is why in this paper, a new data fidelity term is used to take into account of the photonic noise. In this work two data fidelity terms were investigated: a weighted least squares (WLS) term, adapted to Gaussian noise, and the Kullback-Leibler distance (KL), adapted to Poisson noise. A regularized Gauss-Newton algorithm minimizes the cost function iteratively. Both methods decompose materials from a numerical phantom of a mouse. Soft tissues and bones are decomposed in the projection domain; then a tomographic reconstruction creates a 3D material density volume for each material. Comparing relative errors, KL is shown to outperform WLS for low photon counts, in 2D and 3D. This new method could be of particular interest when low-dose acquisitions are performed.

Domaines: Imagerie; Traitement du signal et de l'image [eess.SP]

Tom Hohweiller, Nicolas Ducros, Françoise Peyrin, Bruno Sixou. A Kullback-Leibler approach for 3D reconstruction of spectral CT data corrupted by Poisson noise. SPIE: Optics + Photonics, Aug 2017, San Diego, United States. ⟨hal-01557381v2⟩