Dr. Mai Quyen Pham Profile

Dr. Mai Quyen Pham

at Univ Grenoble-Alpes

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Proceedings Article | 9 March 2017 Paper

A BVMF-B algorithm for nonconvex nonlinear regularized decomposition of spectral x-ray projection images

Mai Quyen Pham, Nicolas Ducros, Barbara Nicolas

Proceedings Volume 10132, 101323K (2017) https://doi.org/10.1117/12.2255656

KEYWORDS: Bone, Gadolinium, Tissues, Photon counting, Reconstruction algorithms, Detection and tracking algorithms, Computed tomography, Tomography, Inverse problems, Sensors, Computer simulations, X-ray imaging, X-rays

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Spectral computed tomography (CT) exploits the measurements obtained by a photon counting detector to reconstruct the chemical composition of an object. In particular, spectral CT has shown a very good ability to image K-edge contrast agent. Spectral CT is an inverse problem that can be addressed solving two subproblems, namely the basis material decomposition (BMD) problem and the tomographic reconstruction problem. In this work, we focus on the BMD problem, which is ill-posed and nonlinear. The BDM problem is classically either linearized, which enables reconstruction based on compressed sensing methods, or nonlinearly solved with no explicit regularization scheme. In a previous communication, we proposed a nonlinear regularized Gauss-Newton (GN) algorithm.¹ However, this algorithm can only be applied to convex regularization functionals. In particular, the ℓ_p (p < 1) norm or the `0 quasi-norm, which are known to provider sparse solutions, cannot be considered. In order to better promote the sparsity of contrast agent images, we propose a nonlinear reconstruction framework that can handle nonconvex regularization terms. In particular, the ℓ₁/ℓ₂ norm ratio is considered.² The problem is solved iteratively using the block variable metric forward-backward (BVMF-B) algorithm,³ which can also enforce the positivity of the material images. The proposed method is validated on numerical data simulated in a thorax phantom made of soft tissue, bone and gadolinium, which is scanned with a 90-kV x-ray tube and a 3-bin photon counting detector.

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