Statistical image reconstruction methods for X-ray computed tomography (CT) provide improved spatial resolution and noise properties over conventional filtered back-projection (FBP) reconstruction, along with other potential advantages such as reduced patient dose and artifacts. Conventional regularized image reconstruction leads to spatially variant spatial resolution and noise characteristics because of interactions between the system models and the regularization. Previous regularization design methods aiming to solve such issues mostly rely on circulant approximations of the Fisher information matrix that are very inaccurate for undersampled geometries like short-scan cone-beam CT. This paper extends the regularization method proposed in [1] to 3D cone-beam CT by introducing a hypothetical scanning geometry that helps address the sampling properties. The proposed regularization designs were compared with the original method in [1] with both phantom simulation and clinical reconstruction in 3D axial X-ray CT. The proposed regularization methods yield improved spatial resolution or noise uniformity in statistical image reconstruction for short-scan axial cone-beam CT.

Conventional ordered-subsets (OS) methods for regularized image reconstruction involve computing the gradient of the regularizer for every subset update. When dealing with large problems with many subsets, such as in 3D X-ray CT, computing the gradient for each subset update can be very computationally expensive. To mitigate this issue, some investigators use unregularized iterations followed by a denoising operation after updating all subsets.1 Although such methods save computation, their convergence properties are uncertain, and since they may not be minimizing any particular cost function it becomes more difficult to design regularization parameters. Furthermore, it is known that inserting filtering steps into unregularized algorithms can lead to undesirable spatial resolution properties.2 Our goal here is to reduce the computational cost without inducing such problems. We propose a new OS-type algorithm that is derived using optimization transfer principles. The proposed method allows the gradient of the regularizer to be updated less frequently, and thus reduces the computational expense when many subsets are used. Our derivation leads to a correction term that accounts for the fact that the regularizer gradient is updated less frequent than every sub-iteration. Simulations and a phantom experiment show that the proposed method reconstructed images with compatible image quality within reduced computation time.

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Motion-compensated image reconstruction (MCIR) has been widely studied to reduce artifacts induced by cardiac motion. In this paper, we propose a new approach to estimating the motion of the coronary arteries. We use a simple linear model for the motion of each coronary artery during an axial scan and we estimate the model parameters in the sinogram domain. The purpose of the method is not to estimate the motion of the coronary arteries precisely, but rather to provide good initial estimates for subsequent joint image reconstruction and motion estimation.. The idea was evaluated with a cardiac CT simulation. Simulation results illustrate that our proposed method can provide reasonably good motion estimates that may be useful for initializing the joint estimation of both motion parameters and reconstructed images.