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Title: A content-adaptive unstructured grid based regularized CT reconstruction method with a SART-type preconditioned fixed-point proximity algorithm
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.  more » « less
Award ID(s):
1912958
NSF-PAR ID:
10333654
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Inverse Problems
Volume:
38
Issue:
3
ISSN:
0266-5611
Page Range / eLocation ID:
035005
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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    cOSSCIR reduced the noise standard deviation in the basis images by a factor of two to six compared to that of MLE + TVmin, when both algorithms were constrained to produce images with the same TV. The cOSSCIR images demonstrated qualitatively improved spatial resolution and depiction of fine anatomical detail. The MLE + TVminalgorithm resulted in lower noise standard deviation than cOSSCIR for the virtual monoenergetic images (VMIs) at higher energy levels and constraint settings, while the cOSSCIR VMIs resulted in lower noise standard deviation at lower energy levels and overall higher qualitative spatial resolution. There were no statistically significant differences in the mean values within the bone region of images reconstructed by the studied algorithms. There were statistically significant differences in the mean values within the soft‐tissue region of the reconstructed images, with cOSSCIR producing mean values closer to the expected values.

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