Statistical image reconstruction (SIR) methods have shown potential to substantially improve the image quality of low‐dose x‐ray computed tomography (CT) as compared to the conventional filtered back‐projection (FBP) method. According to the maximuma posteriori(MAP) estimation, theSIRmethods are typically formulated by an objective function consisting of two terms: (a) a data‐fidelity term that models imaging geometry and physical detection processes in projection data acquisition, and (b) a regularization term that reflects prior knowledge or expectations of the characteristics of the to‐be‐reconstructed image.SIRdesires accurate system modeling of data acquisition, while the regularization term also has a strong influence on the quality of reconstructed images. A variety of regularization strategies have been proposed forSIRin the past decades, based on different assumptions, models, and prior knowledge. In this paper, we review the conceptual and mathematical bases of these regularization strategies and briefly illustrate their efficacies inSIRof low‐doseCT.

Markov random field (MRF) model has been widely employed in edge-preserving regional noise smoothing penalty to reconstruct piece-wise smooth images in the presence of noise, such as in low-dose computed tomography (LdCT). While it preserves edge sharpness, its regional smoothing may sacrifice tissue image textures, which have been recognized as useful imaging biomarkers, and thus it may compromise clinical tasks such as differentiating malignant vs. benign lesions, e.g., lung nodules or colon polyps. This study aims to shift the edge-preserving regional noise smoothing paradigm to texture-preserving framework for LdCT image reconstruction while retaining the advantage of MRF's neighborhood system on edge preservation. Specifically, we adapted the MRF model to incorporate the image textures of muscle, fat, bone, lung, etc. from previous full-dose CT (FdCT) scan as a priori knowledge for texture-preserving Bayesian reconstruction of current LdCT images. To show the feasibility of the proposed reconstruction framework, experiments using clinical patient scans were conducted. The experimental outcomes showed a dramatic gain by the a priori knowledge for LdCT image reconstruction using the commonly-used Haralick texture measures. Thus, it is conjectured that the texture-preserving LdCT reconstruction has advantages over the edge-preserving regional smoothing paradigm for texture-specific clinical applications.

Cerebrovascular diseases, i.e., acute stroke, are a common cause of serious long-term disability. Cerebral perfusion computed tomography (CPCT) can provide rapid, highresolution, quantitative hemodynamic maps to assess and stratify perfusion in patients with acute stroke symptoms. However, CPCT imaging typically involves a substantial radiation dose due to its repeated scanning protocol. Therefore, in this work, we present a low-dose CPCT image reconstruction method to yield high-quality CPCT images and high-precision hemodynamic maps by utilizing the great similarity information among the repeated scanned CPCT images. Specifically, a newly developed low-rank tensor decomposition with spatial-temporal total variation (LRTD-STTV) regularization is incorporated into the reconstruction model. In the LRTD-STTV regularization, the tensor Tucker decomposition is used to describe global spatialtemporal correlations hidden in the sequential CPCT images, and it is superior to the matricization model (i.e., low-rank model) that fails to fully investigate the prior knowledge of the intrinsic structures of the CPCT images after vectorizing the CPCT images. Moreover, the spatial-temporal TV regularization is used to characterize the local piecewise smooth structure in the spatial domain and the pixels’ similarity with the adjacent frames in the temporal domain because the intensity at each pixel in CPCT images is similar to its neighbors. Therefore, the presented LRTD-STTV model can efficiently deliver faithful underlying information of the CPCT images and preserve the spatial structures. An efficient alternating direction method of multipliers algorithm is also developed to solve the presented LRTD-STTV model. Extensive experimental results on numerical phantom and patient data clearly demonstrated that the presented model can significantly improve the quality of CPCT images and provide accurate diagnostic features in hemodynamic maps for low-dose cases compared with the existing popular algorithms.

Reducing radiation dose in dual energy computed tomography (DECT) is highly desirable but it may lead to excessive noise in the filtered backprojection (FBP) reconstructed DECT images, which can inevitably increase the diagnostic uncertainty. To obtain clinically acceptable DECT images from low-mAs acquisitions, in this work we develop a novel scheme based on measurement of DECT data. In this scheme, inspired by the success of edge-preserving non-local means (NLM) filtering in CT imaging and the intrinsic characteristics underlying DECT images, i.e. global correlation and non-local similarity, an averaged image induced NLM-based (aviNLM) regularization is incorporated into the penalized weighted least-squares (PWLS) framework. Specifically, the presented NLM-based regularization is designed by averaging the acquired DECT images, which takes the image similarity within the two energies into consideration. In addition, the weighted least-squares term takes into account DECT data-dependent variance. For simplicity, the presented scheme was termed as ‘PWLS-aviNLM’. The performance of the presented PWLS-aviNLM algorithm was validated and evaluated on digital phantom, physical phantom and patient data. The extensive experiments validated that the presented PWLS-aviNLM algorithm outperforms the FBP, PWLS-TV and PWLS-NLM algorithms quantitatively. More importantly, it delivers the best qualitative results with the finest details and the fewest noise-induced artifacts, due to the aviNLM regularization learned from DECT images. This study demonstrated the feasibility and efficacy of the presented PWLS-aviNLM algorithm to improve the DECT reconstruction and resulting material decomposition.

Dynamic cerebral perfusion computed tomography (DCPCT) has the ability to evaluate the hemodynamic information throughout the brain. However, due to multiple 3-D image volume acquisitions protocol, DCPCT scanning imposes high radiation dose on the patients with growing concerns. To address this issue, in this paper, based on the robust principal component analysis (RPCA, or equivalently the low-rank and sparsity decomposition) model and the DCPCT imaging procedure, we propose a new DCPCT image reconstruction algorithm to improve low-dose DCPCT and perfusion maps quality via using a powerful measure, called Kronecker-basis-representation tensor sparsity regularization, for measuring low-rankness extent of a tensor. For simplicity, the first proposed model is termed tensor-based RPCA (T-RPCA). Specifically, the T-RPCA model views the DCPCT sequential images as a mixture of low-rank, sparse, and noise components to describe the maximum temporal coherence of spatial structure among phases in a tensor framework intrinsically. Moreover, the low-rank component corresponds to the “background” part with spatial-temporal correlations, e.g., static anatomical contribution, which is stationary over time about structure, and the sparse component represents the time-varying component with spatial-temporal continuity, e.g., dynamic perfusion enhanced information, which is approximately sparse over time. Furthermore, an improved nonlocal patch-based T-RPCA (NL-T-RPCA) model which describes the 3-D block groups of the “background” in a tensor is also proposed. The NL-T-RPCA model utilizes the intrinsic characteristics underlying the DCPCT images, i.e., nonlocal self-similarity and global correlation. Two efficient algorithms using alternating direction method of multipliers are developed to solve the proposed T-RPCA and NL-T-RPCA models, respectively. Extensive experiments with a digital brain perfusion phantom, preclinical monkey data, and clinical patient data clearly demonstrate that the two proposed models can achieve more gains than the existing popular algorithms in terms of both quantitative and visual quality evaluations from low-dose acquisitions, especially as low as 20 mAs.