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Abstract The goal of this study is to develop a new computed tomography (CT) image reconstruction method, aiming at improving the quality of the reconstructed images of existing methods while reducing computational costs. Existing CT reconstruction is modeled by pixel-based piecewise constant approximations of the integral equation that describes the CT projection data acquisition process. Using these approximations imposes a bottleneck model error and results in a discrete system of a large size. We propose to develop a content-adaptive unstructured grid (CAUG) based regularized CT reconstruction method to address these issues. Specifically, we design a CAUG of the image domain to sparsely represent the underlying image, and introduce a CAUG-based piecewise linear approximation of the integral equation by employing a collocation method. We further apply a regularization defined on the CAUG for the resulting ill-posed linear system, which may lead to a sparse linear representation for the underlying solution. The regularized CT reconstruction is formulated as a convex optimization problem, whose objective function consists of a weighted least square norm based fidelity term, a regularization term and a constraint term. Here, the corresponding weighted matrix is derived from the simultaneous algebraic reconstruction technique (SART). We then develop a SART-type preconditioned fixed-point proximity algorithm to solve the optimization problem. Convergence analysis is provided for the resulting iterative algorithm. Numerical experiments demonstrate the superiority of the proposed method over several existing methods in terms of both suppressing noise and reducing computational costs. These methods include the SART without regularization and with the quadratic regularization, the traditional total variation (TV) regularized reconstruction method and the TV superiorized conjugate gradient method on the pixel grid.
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This content will become publicly available on December 2, 2025
A nonlocal prior in iterative CT reconstruction
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.
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- Award ID(s):
- 2210866
- PAR ID:
- 10576546
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Medical Physics
- Volume:
- 52
- Issue:
- 3
- ISSN:
- 0094-2405
- Format(s):
- Medium: X Size: p. 1436-1453
- Size(s):
- p. 1436-1453
- Sponsoring Org:
- National Science Foundation
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