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Spectral computed tomography (CT) is extension of the conventional single spectral CT (SSCT) along the energy dimension, which achieves superior energy resolution and material distinguishability. However, for the state-of-the-art photon counting detector (PCD) based spectral CT, because the emitted photons with a fixed total number for each X-ray beam are divided into several energy bins, the noise level is increased in each reconstructed channel image, and it further leads to an inaccurate material decomposition. To improve the reconstructed image quality and decomposition accuracy, in this work, we first employ a refined locally linear transform to convert the structural similarity among two-dimensional (2D) spectral CT images to a spectral-dimension gradient sparsity. By combining the gradient sparsity in the spatial domain, a global three-dimensional (3D) gradient sparsity is constructed, then measured with L<sub>1</sub>-, L<sub>0</sub>- and trace-norm, respectively. For each sparsity measurement, we propose the corresponding optimization model, develop the iterative algorithm, and verify the effectiveness and superiority with real datasets.

Refined Locally Linear Transform-Based Spectral-Domain Gradient Sparsity and Its Applications in Spectral CT Reconstruction