High-Quality Parallel-Ray X-Ray CT Back Projection Using Optimized Interpolation

Deep Radon Prior: A fully unsupervised framework for sparse-view CT reconstruction

BACKGROUND

Sparse-view computed tomography (CT) substantially reduces radiation exposure but often introduces severe artifacts that compromise image fidelity. Recent advances in deep learning for solving inverse problems have shown considerable promise in enhancing CT reconstruction; however, most approaches heavily rely on high-quality training datasets and lack interpretability.

METHOD

To address these challenges, this paper introduces a novel, fully unsupervised deep learning framework that mitigates the dependency on extensive labeled data and improves the interpretability of the reconstruction process. Specifically, we propose the Deep Radon Prior (DRP) framework, inspired by the Deep Image Prior (DIP), which integrates a neural network as an implicit prior into the iterative reconstruction process. This integration facilitates the image domain and the Radon domain gradient feedback and progressively optimizes the neural network through multiple stages, effectively narrowing the solution space in the Radon domain for under-constrained imaging protocols.

RESULTS

We discuss the convergence properties of DRP and validate our approach experimentally, demonstrating its ability to produce high-fidelity images while significantly reducing artifacts. Results indicate that DRP achieves comparable or superior performance to supervised methods, thereby addressing the inherent challenges of sparse-view CT and substantially enhancing image quality.

CONCLUSIONS

The introduction of DRP represents a significant advancement in sparse-view CT imaging by leveraging the inherent deep self-correlation of the Radon domain, enabling effective cooperation with neural network manifolds for image reconstruction. This paradigm shift toward fully unsupervised learning offers a scalable and insightful approach to medical imaging, potentially redefining the landscape of CT reconstruction.

Deep Filtered Back Projection for CT Reconstruction

Filtered back projection (FBP) is a classic analytical algorithm for computed tomography (CT) reconstruction, with high computational efficiency. However, images reconstructed by FBP often suffer from excessive noise and artifacts. The original FBP algorithm uses a window function to smooth signals and a linear interpolation to estimate projection values at un-sampled locations. In this study, we propose a novel framework named DeepFBP in which an optimized filter and an optimized nonlinear interpolation operator are learned with neural networks. Specifically, the learned filter can be considered as the product of an optimized window function and the ramp filter, and the learned interpolation can be considered as an optimized way to utilize projection information of nearby locations through nonlinear combination. The proposed method remains the high computational efficiency of the original FBP and achieves much better reconstruction quality at different noise levels. It also outperforms the TV-based statistical iterative algorithm, with computational time being reduced in an order of two, and state-of-the-art post-processing deep learning methods that have deeper and more complicated network structures.

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).

Exact gram filtering and efficient back projection for iterative CT reconstruction

PURPOSE

Forward and back-projections are the basis of all model-based iterative reconstruction (MBIR) methods. However, computing these accurately is time consuming. In this paper, we present a method for model-based iterative reconstruction in parallel X-ray beam geometry that utilizes a Gram filter to efficiently implement forward and back projection.

METHODS

We propose using voxel-basis and modeling its footprint in a box spline framework to calculate the Gram filter exactly and improve the performance of back-projection. In the special case of parallel X-ray beam geometry, the forward and back-projection can be implemented by an estimated Gram filter efficiently if the sinogram signal is bandlimited. In this paper, a specialized sinogram interpolation method is proposed to eliminate the bandlimited prerequisite and thus improve the reconstruction accuracy. We build on this idea by utilizing the continuity of the voxel-basis' footprint, which provides a more accurate sinogram interpolation and further improves the efficiency and quality of back-projection. In addition, the detector blur effect can be efficiently accounted for in our method to better handle realistic scenarios.

RESULTS

The proposed method is tested on both phantom and real CT images under different resolutions, sinogram sampling steps, and noise levels. The proposed method consistently outperforms other state-of-the-art projection models in terms of speed and accuracy for both back-projection and reconstruction.

CONCLUSIONS

We proposed a iterative reconstruction methodology for 3D parallel-beam X-ray CT reconstruction. Our experimental results demonstrate that the proposed methodology is accurate, fast, and reproducible, and outperforms alternative state-of-the-art projection models on both back-projection and reconstruction results significantly. This article is protected by copyright. All rights reserved.

Label enhanced and patch based deep learning for phase retrieval from single frame fringe pattern in fringe projection 3D measurement

We propose a label enhanced and patch based deep learning phase retrieval approach which can achieve fast and accurate phase retrieval using only several fringe patterns as training dataset. To the best of our knowledge, it is the first time that the advantages of the label enhancement and patch strategy for deep learning based phase retrieval are demonstrated in fringe projection. In the proposed method, the enhanced labeled data in training dataset is designed to learn the mapping between the input fringe pattern and the output enhanced fringe part of the deep neural network (DNN). Moreover, the training data is cropped into small overlapped patches to expand the training samples for the DNN. The performance of the proposed approach is verified by experimental projection fringe patterns with applications in dynamic fringe projection 3D measurement.

Direct generation of starting points for freeform off-axis three-mirror imaging system design using neural network based deep-learning

In this paper, we propose a framework of starting points generation for freeform reflective triplet using back-propagation neural network based deep-learning. The network is trained using various system specifications and the corresponding surface data obtained by system evolution as the data set. Good starting points of specific system specifications for further optimization can be generated immediately using the obtained network in general. The feasibility of this design process is validated by designing the Wetherell-configuration freeform off-axis reflective triplet. The amount of time and human effort as well as the dependence on advanced design skills are significantly reduced. These results highlight the powerful ability of deep learning in the field of freeform imaging optical design.

Piston sensing of sparse aperture systems with a single broadband image via deep learning

The pistons of sparse aperture systems need to be controlled within a fraction of a wavelength for the system's optimal imaging performance. In this paper, we demonstrate that deep learning is capable of performing piston sensing with a single wide-band image after appropriate training. Taking the sensing issue as a fitting task, the deep learning-based method utilizes a deep convolutional neural network to learn complex input-output mapping relations between the broadband intensity distributions and corresponding piston values. Given a trained network and one broadband focal intensity image as the input, the piston can be obtained directly and the capture range achieving the coherence length of the broadband light is available. Simulations and experiments demonstrate the validity of the proposed method. Using only in-focused broadband images as the inputs without defocus division and wavelength dispersion, obviously relaxes the optics complexity. In view of the efficiency and superiority, it's expected that the method proposed in this paper may be widely applied in multi-aperture imaging.

One-step robust deep learning phase unwrapping

Phase unwrapping is an important but challenging issue in phase measurement. Even with the research efforts of a few decades, unfortunately, the problem remains not well solved, especially when heavy noise and aliasing (undersampling) are present. We propose a database generation method for phase-type objects and a one-step deep learning phase unwrapping method. With a trained deep neural network, the unseen phase fields of living mouse osteoblasts and dynamic candle flame are successfully unwrapped, demonstrating that the complicated nonlinear phase unwrapping task can be directly fulfilled in one step by a single deep neural network. Excellent anti-noise and anti-aliasing performances outperforming classical methods are highlighted in this paper.