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

Mai Quyen Pham; Nicolas Ducros; Barbara Nicolas

doi:10.1117/12.2255656

9 March 2017 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, Medical Imaging 2017: Physics of Medical Imaging; 101323K (2017) https://doi.org/10.1117/12.2255656
Event: SPIE Medical Imaging, 2017, Orlando, Florida, United States

Abstract

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.

Citation Download Citation

Mai Quyen Pham, Nicolas Ducros, and Barbara Nicolas "A BVMF-B algorithm for nonconvex nonlinear regularized decomposition of spectral x-ray projection images", Proc. SPIE 10132, Medical Imaging 2017: Physics of Medical Imaging, 101323K (9 March 2017); https://doi.org/10.1117/12.2255656

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