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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Cooling Improves Cosmic Microwave Background Map-making when Low-frequency Noise is Large
In the context of cosmic microwave background data analysis, we study the solution to the equation that transforms scanning data into a map. As originally suggested in “messenger” methods for solving linear systems, we split the noise covariance into uniform and nonuniform parts and adjust their relative weights during the iterative solution. With simulations, we study mock instrumental data with different noise properties, and find that this “cooling” or perturbative approach is particularly effective when there is significant low-frequency noise in the timestream. In such cases, a conjugate gradient algorithm applied to this modified system converges faster and to a higher fidelity solution than the standard conjugate gradient approach. We give an analytic estimate for the parameter that controls how gradually the linear system should change during the course of the solution.
more » « less- Award ID(s):
- 1815887
- NSF-PAR ID:
- 10360355
- Publisher / Repository:
- DOI PREFIX: 10.3847
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 922
- Issue:
- 2
- ISSN:
- 0004-637X
- Format(s):
- Medium: X Size: Article No. 97
- Size(s):
- ["Article No. 97"]
- Sponsoring Org:
- National Science Foundation
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Purpose To develop a non‐Cartesian k‐space reconstruction method using self‐calibrated region‐specific interpolation kernels for highly accelerated acquisitions.
Methods In conventional non‐Cartesian GRAPPA with through‐time GRAPPA (TT‐GRAPPA), the use of region‐specific interpolation kernels has demonstrated improved reconstruction quality in dynamic imaging for highly accelerated acquisitions. However, TT‐GRAPPA requires the acquisition of a large number of separate calibration scans. To reduce the overall imaging time, we propose Self‐calibrated Interpolation of Non‐Cartesian data with GRAPPA (SING) to self‐calibrate region‐specific interpolation kernels from dynamic undersampled measurements. The SING method synthesizes calibration data to adapt to the distinct shape of each region‐specific interpolation kernel geometry, and uses a novel local k‐space regularization through an extension of TT‐GRAPPA. This calibration approach is used to reconstruct non‐Cartesian images at high acceleration rates while mitigating noise amplification. The reconstruction quality of SING is compared with conjugate‐gradient SENSE and TT‐GRAPPA in numerical phantoms and in vivo cine data sets.
Results In both numerical phantom and in vivo cine data sets, SING offers visually and quantitatively similar reconstruction quality to TT‐GRAPPA, and provides improved reconstruction quality over conjugate‐gradient SENSE. Furthermore, temporal fidelity in SING and TT‐GRAPPA is similar for the same acceleration rates. G‐factor evaluation over the heart shows that SING and TT‐GRAPPA provide similar noise amplification at moderate and high rates.
Conclusion The proposed SING reconstruction enables significant improvement of acquisition efficiency for calibration data, while matching the reconstruction performance of TT‐GRAPPA.
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