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FONT-SIR: Fourth-Order Nonlocal Tensor Decomposition Model for Spectral CT Image Reconstruction

Spectral computed tomography (CT) reconstructs images from different spectral data through photon counting detectors (PCDs). However, due to the limited number of photons and the counting rate in the corresponding spectral segment, the reconstructed spectral images are usually affected by severe noise. In this paper, we propose a fourth-order nonlocal tensor decomposition model for spectral CT image reconstruction (FONT-SIR). To maintain the original spatial relationships among similar patches and improve the imaging quality, similar patches without vectorization are grouped in both spectral and spatial domains simultaneously to form the fourth-order processing tensor unit. The similarity of different patches is measured with the cosine similarity of latent features extracted using principal component analysis (PCA). By imposing the constraints of the weighted nuclear and total variation (TV) norms, each fourth-order tensor unit is decomposed into a low-rank component and a sparse component, which can efficiently remove noise and artifacts while preserving the structural details. Moreover, the alternating direction method of multipliers (ADMM) is employed to solve the decomposition model. Extensive experimental results on both simulated and real data sets demonstrate that the proposed FONT-SIR achieves superior qualitative and quantitative performance compared with several state-of-the-art methods.