A Look-Up Table-Based Ray Integration Framework for 2-D/3-D Forward and Back Projection in X-Ray CT

Trapezoidal back projection for positron emission tomography reconstruction

BACKGROUND

In the back projection step of the 3D PET reconstruction, all Lines of Responses (LORs) that go through a given voxel need to be identified and included in an integral. The standard Monte Carlo solution to this task samples stochastically the surfaces of the detector crystals and the volume of the voxel to search for valid LORs. To get a low noise Monte Carlo estimate, the number of samples needs to be very high, making the computational cost of the projection significant. In this paper, a novel deterministic projection algorithm called trapezoidal back projection (TBP) is proposed that replaces the extensive Monte Carlo sampling. Its goal is to determine all LORs that contribute to a given voxel together with their exact contribution weights. This is achieved by trapezoidal rasterization and a pre-computed look-up table.

RESULTS

The precision and speed of the proposed TBP algorithm were compared to that of the Monte Carlo back projection of 1000, 10,000 and 100,000 samples. Measurements were run on a National Electrical Manufacturers Association (NEMA) NU 4-2008 image quality phantom as well as on a mouse acquisition. Results show that the TBP algorithm achieves the same low noise level (2.5 Uniformity %STD) as the Monte Carlo method with the highest sample number, but 13 times faster-the highest-precision Monte Carlo back projection takes 31.3 s, while TBP takes only 2.3 s on the NEMA NU 4-2008 image quality phantom of 200 × 200 × 333 voxels.

CONCLUSION

The proposed deterministic TBP algorithm achieves a low noise level in a short runtime, thus it can be a promising solution for the back projection of the 3D PET reconstruction. Its performance advantage could be used to reduce either the reconstruction time, the data acquisition time, or the noise level of the image.

RBP-DIP: Residual back projection with deep image prior for ill-posed CT reconstruction

The success of deep image prior (DIP) in a number of image processing tasks has motivated their application in image reconstruction problems in computed tomography (CT). In this paper, we introduce a residual back projection technique (RBP) that improves the performance of deep image prior framework in iterative CT reconstruction, especially when the reconstruction problem is highly ill-posed. The RBP-DIP framework uses an untrained U-net in conjunction with a novel residual back projection connection to minimize the objective function while improving reconstruction accuracy. In each iteration, the weights of the untrained U-net are optimized, and the output of the U-net in the current iteration is used to update the input of the U-net in the next iteration through the proposed RBP connection. The introduction of the RBP connection strengthens the regularization effects of the DIP framework in the context of iterative CT reconstruction leading to improvements in accuracy. Our experiments demonstrate that the RBP-DIP framework offers improvements over other state-of-the-art conventional IR methods, as well as pre-trained and untrained models with similar network structures under multiple conditions. These improvements are particularly significant in the few-view and limited-angle CT reconstructions, where the corresponding inverse problems are highly ill-posed and the training data is limited. Furthermore, RBP-DIP has the potential for further improvement. Most existing IR algorithms, pre-trained models, and enhancements applicable to the original DIP algorithm can also be integrated into the RBP-DIP framework.

Total Deep Variation: A Stable Regularization Method for Inverse Problems

Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and a regularizer. Classically, handcrafted regularizers are used, which are commonly outperformed by state-of-the-art deep learning approaches. In this work, we combine the variational formulation of inverse problems with deep learning by introducing the data-driven general-purpose total deep variation regularizer. In its core, a convolutional neural network extracts local features on multiple scales and in successive blocks. This combination allows for a rigorous mathematical analysis including an optimal control formulation of the training problem in a mean-field setting and a stability analysis with respect to the initial values and the parameters of the regularizer. In addition, we experimentally verify the robustness against adversarial attacks and numerically derive upper bounds for the generalization error. Finally, we achieve state-of-the-art results for several imaging tasks.

Sparse-view and limited-angle CT reconstruction with untrained networks and deep image prior

BACKGROUND AND OBJECTIVE

Neural network based image reconstruction methods are becoming increasingly popular. However, limited training data and the lack of theoretical guarantees for generalizability raised concerns, especially in biomedical imaging applications. These challenges are known to lead to an unstable reconstruction process that poses significant problems in biomedical image reconstruction. In this paper, we present a new framework that uses untrained generator networks to tackle this challenge, leveraging the structure of deep networks for regularizing solutions based on a technique known as Deep Image Prior (DIP).

METHODS

To achieve a high reconstruction accuracy, we propose a framework optimizing both the latent vector and the weights of a generator network during the reconstruction process. We also propose the corresponding reconstruction strategies to improve the stability and convergent performance of the proposed framework. Furthermore, instead of calculating forward projection in each iteration, we propose implementing its normal operator as a convolutional kernel under parallel beam geometry, thus greatly accelerating the calculation.

RESULTS

Our experiments show that the proposed framework has significant improvements over other state-of-the-art conventional, pre-trained, and untrained methods under sparse-view, limited-angle, and low-dose conditions.

CONCLUSIONS

Applying to parallel beam X-ray imaging, our framework shows advantages in speed, accuracy, and stability of the reconstruction process. We also show that the proposed framework is compatible with all differentiable regularizations that are commonly used in biomedical image reconstruction literature. Our framework can also be used as a post-processing technique to further improve the reconstruction generated by any other reconstruction methods. Furthermore, the proposed framework requires no training data and can be adjusted on-demand to adapt to different conditions (e.g. noise level, geometry, and imaged object).

Projection-to-image transform frame: a lightweight block reconstruction network (LBRN) for computed tomography

To solve the problem of learning based computed tomography (CT) reconstruction, several reconstruction networks were invented. However, applying neural network to tomographic reconstruction still remains challenging due to unacceptable memory space requirement. In this study, we presents a novel lightweight block reconstruction network (LBRN), which transforms the reconstruction operator into a deep neural network by unrolling the filter back-projection (FBP) method. Specifically, the proposed network contains two main modules, which, respectively, correspond to the filter and back-projection of FBP method. The first module of LBRN decouples the relationship of Radon transform between the reconstructed image and the projection data. Therefore, the following module, block back-projection module, can use the block reconstruction strategy. Due to each image block is only connected with part filtered projection data, the network structure is greatly simplified and the parameters of the whole network is dramatically reduced. Moreover, this approach is trained end-to-end, working directly from raw projection data and does not depend on any initial images. Five reconstruction experiments are conducted to evaluate the performance of the proposed LBRN: full angle, low-dose CT, region of interest (ROI), metal artifacts reduction and real data experiment. The results of the experiments show that the LBRN can be effectively introduced into the reconstruction process and has outstanding advantages in terms of different reconstruction problems.

Artificial intelligence in radiotherapy: a technological review

Radiation therapy (RT) is widely used to treat cancer. Technological advances in RT have occurred in the past 30 years. These advances, such as three-dimensional image guidance, intensity modulation, and robotics, created challenges and opportunities for the next breakthrough, in which artificial intelligence (AI) will possibly play important roles. AI will replace certain repetitive and labor-intensive tasks and improve the accuracy and consistency of others, particularly those with increased complexity because of technological advances. The improvement in efficiency and consistency is important to manage the increasing cancer patient burden to the society. Furthermore, AI may provide new functionalities that facilitate satisfactory RT. The functionalities include superior images for real-time intervention and adaptive and personalized RT. AI may effectively synthesize and analyze big data for such purposes. This review describes the RT workflow and identifies areas, including imaging, treatment planning, quality assurance, and outcome prediction, that benefit from AI. This review primarily focuses on deep-learning techniques, although conventional machine-learning techniques are also mentioned.