Sparse-view X-ray spectral CT reconstruction using annihilating filter-based low rank hankel matrix approach

Abstract

In a kVp switching-based sparse view spectral CT, each spectral image cannot be reconstructed separably by an analytic reconstruction method, because the projection views for each spectral band is too sparse. However, the underlying structure is common between the spectral bands, so there exists inter-spectral redundancies that can be exploited by the recently proposed annihilating filter-based low rank Hankel matrix approach (ALOHA). More specifically, the sparse view projection data are first rebinned in the Fourier space, from which Hankel structured matrix with missing elements are constructed for each spectral band. Thanks to the inter-spectral correlations as well as transform domain sparsity of underlying images, the concatenated Hankel structured matrix is low-ranked, and the missing Fourier data for each spectral band can be simultaneously estimated using a low rank matrix completion. To reduce the computational complexity furthermore, we exploit the Hermitian symmetry of Fourier data. Numerical experiments confirm that the proposed method outperforms the existing ones.