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Abstract BackgroundComputed tomography (CT) reconstruction problems are always framed as inverse problems, where the attenuation map of an imaged object is reconstructed from the sinogram measurement. In practice, these inverse problems are often ill‐posed, especially under few‐view and limited‐angle conditions, which makes accurate reconstruction challenging. Existing solutions use regularizations such as total variation to steer reconstruction algorithms to the most plausible result. However, most prevalent regularizations rely on the same priors, such as piecewise constant prior, hindering their ability to collaborate effectively and further boost reconstruction precision. PurposeThis study aims to overcome the aforementioned challenge a prior previously limited to discrete tomography. This enables more accurate reconstructions when the proposed method is used in conjunction with most existing regularizations as they utilize different priors. The improvements will be demonstrated through experiments conducted under various conditions. MethodsInspired by the discrete algebraic reconstruction technique (DART) algorithm for discrete tomography, we find out that pixel grayscale values in CT images are not uniformly distributed and are actually highly clustered. Such discovery can be utilized as a powerful prior for CT reconstruction. In this paper, we leverage the collaborative filtering technique to enable the collaboration of the proposed prior and most existing regularizations, significantly enhancing the reconstruction accuracy. ResultsOur experiments show that the proposed method can work with most existing regularizations and significantly improve the reconstruction quality. Such improvement is most pronounced under limited‐angle and few‐view conditions. Furthermore, the proposed regularization also has the potential for further improvement and can be utilized in other image reconstruction areas. ConclusionsWe propose improving the performance of iterative CT reconstruction algorithms by applying the collaborative filtering technique along with a prior based on the densely clustered distribution of pixel grayscale values in CT images. Our experimental results indicate that the proposed methodology consistently enhances reconstruction accuracy when used in conjunction with most existing regularizations, particularly under few‐view and limited‐angle conditions. 

Abstract PurposeForward and backprojections are the basis of all model‐based iterative reconstruction (MBIR) methods. However, computing these accurately is time‐consuming. In this paper, we present a method for MBIR in parallel X‐ray beam geometry that utilizes a Gram filter to efficiently implement forward and backprojection. MethodsWe propose using voxel‐basis and modeling its footprint in a box spline framework to calculate the Gram filter exactly and improve the performance of backprojection. In the special case of parallel X‐ray beam geometry, the forward and backprojection can be implemented by an estimated Gram filter efficiently if the sinogram signal is bandlimited. In this paper, a specialized sinogram interpolation method is proposed to eliminate the bandlimited prerequisite and thus improve the reconstruction accuracy. We build on this idea by utilizing the continuity of the voxel‐basis' footprint, which provides a more accurate sinogram interpolation and further improves the efficiency and quality of backprojection. In addition, the detector blur effect can be efficiently accounted for in our method to better handle realistic scenarios. ResultsThe proposed method is tested on both phantom and real computed tomography (CT) images under different resolutions, sinogram sampling steps, and noise levels. The proposed method consistently outperforms other state‐of‐the‐art projection models in terms of speed and accuracy for both backprojection and reconstruction. ConclusionsWe proposed a iterative reconstruction methodology for 3D parallel‐beam X‐ray CT reconstruction. Our experimental results demonstrate that the proposed methodology is accurate, fast, and reproducible, and outperforms alternative state‐of‐the‐art projection models on both backprojection and reconstruction results significantly.