Spectral computed tomography (CT) reconstructs material-dependent attenuation images from the projections of multiple narrow energy windows which is meaningful for material identification and decomposition. Unfortunately, the multi-energy projection datasets usually have lower signal-noise-ratios (SNR). Very recently, a spatial-spectral cube matching frame (SSCMF) was proposed to explore the non-local spatial-spectral similarities for spectral CT. This method constructs a group by clustering up a series of non-local spatial-spectral cubes. The small size of spatial patches for such a group makes the SSCMF fail to fully encode the sparsity and low-rank properties. The hard-thresholding and collaboration filtering in the SSCMF also cause difficulty in recovering the image features and spatial edges. While all the steps are operated on 4-D group, the huge computational cost and memory load might not be affordable in practice. To avoid the above limitations and further improve image quality, we first formulate a non-local cube-based tensor instead of group to encode the sparsity and low-rank properties. Then, as a new regularizer, the Kronecker- Basis-Representation (KBR) tensor factorization is employed into a basic spectral CT reconstruction model to enhance the capability of image feature extraction and spatial edge preservation, generating a non-local low-rank cube-based tensor factorization (NLCTF) method. Finally, the split-Bregman method is adopted to solve the NLCTF model. Both numerical simulations and preclinical mouse studies are performed to validate and evaluate the NLCTF algorithm. The results show that the NLCTF method outperforms other state-of-the-art competing algorithms.

Limited-angle x-ray computed tomography (CT) reconstruction is a typical ill-posed problem. To recover satisfied reconstructed images with limited-angle CT projections, prior information is usually introduced into image reconstruction, such as the piece-wise constant, non-local image similarity and so on. To further improve the image quality for limited-angle CT reconstruction, the dictionary learning and image gradient ℓ0-norm are combined into image reconstruction model, it can be called as ℓ0 DL reconstruction technique. The advantages of ℓ0 DL can be divided into two aspects. On one hand, the proposed ℓ0 DL method can inherit the advantages of dictionary learning in image details preservation and features recovery by exploring an over-complete dictionary. On the other hand, the image gradient ℓ0-norm minimization can further protect image edges and reduce shadow artifact. Both numerical simulation and preclinical mouse experiments are performed to validate and evaluate the outperformances of proposed ℓ0 DL method by comparing with other state-of-the-art methods, such as total variation (TV) minimization and TV with low rank (TV + LR).

Spectral computed tomography (CT) reconstructs multienergy images from data in different energy bins. However, these reconstructed images can be contaminated by noise due to the limited numbers of photons in the corresponding energy bins. In this paper, we propose a spectral CT reconstruction method aided by self-similarity in image-spectral tensors, which utilizes the selfsimilarity of patches in both spatial and spectral domains. Patches with similar structures identified by a joint spatial and spectral searching strategy form a basic tensor unit, and can be utilized to improve image quality. Specifically, each tensor is decomposed into a low-rank component and a sparse component, which respectively represent the stable structures and feature differences across different energy bins. The augmented Lagrange method is applied to optimize the proposed objective function. To validate the performance of the proposed method, several simulated clinical and real data experiments are performed. The qualitative and quantitative results demonstrate that the proposed method outperforms several representative state-of-the-art algorithms in terms of preserving image details and reducing artifacts.

The spectral computed tomography (CT) has huge advantages by providing accurate material information. Unfortunately, due to the instability or overdetermination of the material decomposition model, the accuracy of material decomposition can be compromised in practice. Very recently, the dictionary learning-based image-domain material decomposition (DLIMD) can obtain high accuracy for material decompositions from reconstructed spectral CT images. This method can explore the correlation of material components to some extent by training a unified dictionary from all material images. In addition, the dictionary learning-based prior as a penalty is applied on material components independently, and many parameters would be carefully elaborated in practice. Because the concentration of contrast agent in clinical applications is low, it can result in data inconsistency for dictionary-based representation during the iteration process. To avoid the aforementioned limitations and further improve the accuracy of materials, we first construct a generalized DLIMD (GDLIMD) model. Then, the material tensor image is unfolded along the mode-1 to enhance the correlation of different materials. Finally, to avoid the data inconsistency of low iodine contrast, a normalization strategy is employed. Both physical phantom and tissue-synthetic phantom experiments demonstrate the proposed GDLIMD method outperforms the DLIMD and direct inversion (DI) methods.

The photon-counting detector based spectral computed tomography (CT) is promising for lesion detection, tissue characterization, and material decomposition. However, the lower signal-to-noise ratio within multi-energy projection dataset can result in poorly reconstructed image quality. Recently, as prior information, a high-quality spectral mean image was introduced into the prior image constrained compressed sensing (PICCS) framework to suppress noise, leading to spectral PICCS (SPICCS). In the original SPICCS model, the image gradient L ₁ -norm is employed, and it can cause blurred edge structures in the reconstructed images. Encouraged by the advantages in edge preservation and finer structure recovering, the image gradient L ₀ -norm was incorporated into the PICCS model. Furthermore, due to the difference of energy spectrum in different channels, a weighting factor is introduced and adaptively adjusted for different channel-wise images, leading to an L ₀ -norm based adaptive SPICCS (L ₀ -ASPICCS) algorithm for low-dose spectral CT reconstruction. The split-Bregman method is employed to minimize the objective function. Extensive numerical simulations and physical phantom experiments are performed to evaluate the proposed method. By comparing with the state-of-the-art algorithms, such as the simultaneous algebraic reconstruction technique, total variation minimization, and SPICCS, the advantages of our proposed method are demonstrated in terms of both qualitative and quantitative evaluation results.