The development of computed tomography (CT) image reconstruction methods that significantly reduce patient radiation exposure, while maintaining high image quality is an important area of research in low-dose CT imaging. We propose a new penalized weighted least squares (PWLS) reconstruction method that exploits regularization based on an efficient Union of Learned TRAnsforms (PWLS-ULTRA). The union of square transforms is pre-learned from numerous image patches extracted from a dataset of CT images or volumes. The proposed PWLS-based cost function is optimized by alternating between a CT image reconstruction step, and a sparse coding and clustering step. The CT image reconstruction step is accelerated by a relaxed linearized augmented Lagrangian method with ordered-subsets that reduces the number of forward and back projections. Simulations with 2-D and 3-D axial CT scans of the extended cardiac-torso phantom and 3-D helical chest and abdomen scans show that for both normal-dose and low-dose levels, the proposed method significantly improves the quality of reconstructed images compared to PWLS reconstruction with a nonadaptive edge-preserving regularizer. PWLS with regularization based on a union of learned transforms leads to better image reconstructions than using a single learned square transform. We also incorporate patch-based weights in PWLS-ULTRA that enhance image quality and help improve image resolution uniformity. The proposed approach achieves comparable or better image quality compared to learned overcomplete synthesis dictionaries, but importantly, is much faster (computationally more efficient).

Obtaining accurate and reliable images from low-dose computed tomography (CT) is challenging. Regression convolutional neural network (CNN) models that are learned from training data are increasingly gaining attention in low-dose CT reconstruction. This paper modifies the architecture of an iterative regression CNN, BCD-Net, for fast, stable, and accurate low-dose CT reconstruction, and presents the convergence property of the modified BCD-Net. Numerical results with phantom data show that applying faster numerical solvers to modelbased image reconstruction (MBIR) modules of BCD-Net leads to faster and more accurate BCD-Net; BCD-Net significantly improves the reconstruction accuracy, compared to the state-of-the-art MBIR method using learned transforms; BCD-Net achieves better image quality, compared to a state-of-the-art iterative NN architecture, ADMM-Net. Numerical results with clinical data show that BCD-Net generalizes significantly better than a state-of-the-art deep (non-iterative) regression NN, FBP-ConvNet, that lacks MBIR modules. The authors indicated by asterisks ( * ) equally contributed to this work. Corresponding author: Yong Long (email: yong.long@sjtu.edu.cn). This paper has supplementary document. The prefix "S" indicates the numbers in figure and section in the supplementary document. arXiv:1908.01287v1 [eess.IV] 4 Aug 2019 2 I.Y. Chun and X. Zheng et al.solving large-scale inverse problems in imaging, the first scheme is limited in training CNNs from large-scale images; the second scheme does not effectively remove complicated noise features; and the third scheme has limited benefits when applied to convolutional layers.An alternative way to regulate overfitting of regression CNNs in inverse imaging problems is combining them with model-based image reconstruction (MBIR) that considers imaging physics or image formation models, and noise statistics in measurements. is an iterative regression CNN that generalizes a block coordinate descent (BCD) MBIR method using learned convolutional regularizers [5]. Each layer (or iteration) of BCD-Net consists of image denoising and MBIR modules. In particular, the denoising modules use layer-wise regression CNNs to effectively remove layer-dependent noise features. Many existing works can be viewed as a special case of BCD-Net. For example, RED [11] and MoDL [1] are special cases of BCD-Net, because they use identical image denoising modules across layers or only consider quadratic data-fidelity terms (e.g., the first term in (P1)) in their MBIR modules.This paper modifies BCD-Net that uses convolutional autoencoders in its denoising modules [4], and applies the modified BCD-Net to low-dose CT reconstruction. First, for fast CT reconstruction, we apply the Accelerated Proximal Gradient method using a Majorizer (APG-M), e.g., FISTA [2], to MBIR modules using the statistical CT data-fidelity term. Second, this paper provides the sequence convergence guarantee of BCD-Net when applied to low-dose CT reconstruction. Third, it investigates the generalization ca...

A major challenge in computed tomography (CT) is to reduce X-ray dose to a low or even ultra-low level while maintaining the high quality of reconstructed images. We propose a new method for CT reconstruction that combines penalized weighted-least squares reconstruction (PWLS) with regularization based on a sparsifying transform (PWLS-ST) learned from a dataset of numerous CT images. We adopt an alternating algorithm to optimize the PWLS-ST cost function that alternates between a CT image update step and a sparse coding step. We adopt a relaxed linearized augmented Lagrangian method with ordered-subsets (relaxed OS-LALM) to accelerate the CT image update step by reducing the number of forward and backward projections. Numerical experiments on the XCAT phantom show that for low dose levels, the proposed PWLS-ST method dramatically improves the quality of reconstructed images compared to PWLS reconstruction with a nonadaptive edge-preserving regularizer (PWLS-EP).

A major challenge in X-ray computed tomography (CT) is reducing radiation dose while maintaining high quality of reconstructed images. To reduce the radiation dose, one can reduce the number of projection views (sparse-view CT); however, it becomes difficult to achieve high-quality image reconstruction as the number of projection views decreases. Researchers have applied the concept of learning sparse representations from (highquality) CT image dataset to the sparse-view CT reconstruction. We propose a new statistical CT reconstruction model that combines penalized weighted-least squares (PWLS) and 1 prior with learned sparsifying transform (PWLS-ST-1), and a corresponding efficient algorithm based on Alternating Direction Method of Multipliers (ADMM). To moderate the difficulty of tuning ADMM parameters, we propose a new ADMM parameter selection scheme based on approximated condition numbers. We interpret the proposed model by analyzing the minimum mean square error of its ( 2-norm relaxed) image update estimator. Our results with the extended cardiac-torso (XCAT) phantom data and clinical chest data show that, for sparse-view 2D fanbeam CT and 3D axial cone-beam CT, PWLS-ST-1 improves the quality of reconstructed images compared to the CT reconstruction methods using edge-preserving regularizer and 2 prior with learned ST. These results also show that, for sparse-view 2D fan-beam CT, PWLS-ST-1 achieves comparable or better image quality and requires much shorter runtime than PWLS-DL using a learned overcomplete dictionary. Our results with clinical chest data show that, methods using the unsupervised learned prior generalize better than a state-of-the-art deep "denoising" neural network that does not use a physical imaging model.

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