Framelet tensor sparsity with block matching for spectral CT reconstruction

Spectral computed tomography (CT) based on the photon-counting detection system has the capability to produce energy-discriminative attenuation maps of objects with a single scan. However, the insufficiency of photons collected into the narrow energy bins results in high quantum noise levels causing low image quality. This work aims to improve spectral CT image quality by developing a novel regularization based on framelet tensor prior.First, similar patches are extracted from highly correlated interchannel images in spectral and spatial domains, and stacked to form a third-order tensor after vectorization along the energy channels. Second, the framelet tensor nuclear norm (FTNN) is introduced and applied to construct the regularization to exploit the sparsity embedded in nonlocal similarity of spectral images, and thus the reconstruction problem is modeled as a constrained optimization. Third, an iterative algorithm is proposed by utilizing the alternating direction method of multipliers framework in which efficient solvers are developed for each subproblem.Both numerical simulations and real data verifications were performed to evaluate and validate the proposed FTNN-based method. Compared to the analytic, TV-based, and the state-of-the-art tensor-based methods, the proposed method achieves higher numerical accuracy on both reconstructed CT images and decomposed material maps in the mouse data indicating the capability in noise suppression and detail preservation of the proposed method.A framelet tensor sparsity-based iterative algorithm is proposed for spectral reconstruction. The qualitative and quantitative comparisons show a promising improvement of image quality, indicating its promising potential in spectral CT imaging.