A Compound Gaussian Network for Solving Linear Inverse Problems

For solving linear inverse problems, particularly of the type that appear in tomographic imaging and compressive sensing, this paper develops two new approaches. The first approach is an iterative algorithm that minimizers a regularized least squares objective function where the regularization is based on a compound Gaussian prior distribution. The Compound Gaussian prior subsumes many of the commonly used priors in image reconstruction, including those of sparsity-based approaches. The developed iterative algorithm gives rise to the paper's second new approach, which is a deep neural network that corresponds to an "unrolling" or "unfolding" of the iterative algorithm. Unrolled deep neural networks have interpretable layers and outperform standard deep learning methods. This paper includes a detailed computational theory that provides insight into the construction and performance of both algorithms. The conclusion is that both algorithms outperform other state-of-the-art approaches to tomographic image formation and compressive sensing, especially in the difficult regime of low training.Comment: 13 pages, 7 figures, 5 tables; references update

3D helical CT Reconstruction with a Memory Efficient Learned Primal-Dual Architecture

Deep learning based computed tomography (CT) reconstruction has demonstrated outstanding performance on simulated 2D low-dose CT data. This applies in particular to domain adapted neural networks, which incorporate a handcrafted physics model for CT imaging. Empirical evidence shows that employing such architectures reduces the demand for training data and improves upon generalisation. However, their training requires large computational resources that quickly become prohibitive in 3D helical CT, which is the most common acquisition geometry used for medical imaging. Furthermore, clinical data also comes with other challenges not accounted for in simulations, like errors in flux measurement, resolution mismatch and, most importantly, the absence of the real ground truth. The necessity to have a computationally feasible training combined with the need to address these issues has made it difficult to evaluate deep learning based reconstruction on clinical 3D helical CT. This paper modifies a domain adapted neural network architecture, the Learned Primal-Dual (LPD), so that it can be trained and applied to reconstruction in this setting. We achieve this by splitting the helical trajectory into sections and applying the unrolled LPD iterations to those sections sequentially. To the best of our knowledge, this work is the first to apply an unrolled deep learning architecture for reconstruction on full-sized clinical data, like those in the Low dose CT image and projection data set (LDCT). Moreover, training and testing is done on a single GPU card with 24GB of memory

Robust Single-view Cone-beam X-ray Pose Estimation with Neural Tuned Tomography (NeTT) and Masked Neural Radiance Fields (mNeRF)

Many tasks performed in image-guided, mini-invasive, medical procedures can be cast as pose estimation problems, where an X-ray projection is utilized to reach a target in 3D space. Expanding on recent advances in the differentiable rendering of optically reflective materials, we introduce new methods for pose estimation of radiolucent objects using X-ray projections, and we demonstrate the critical role of optimal view synthesis in performing this task. We first develop an algorithm (DiffDRR) that efficiently computes Digitally Reconstructed Radiographs (DRRs) and leverages automatic differentiation within TensorFlow. Pose estimation is performed by iterative gradient descent using a loss function that quantifies the similarity of the DRR synthesized from a randomly initialized pose and the true fluoroscopic image at the target pose. We propose two novel methods for high-fidelity view synthesis, Neural Tuned Tomography (NeTT) and masked Neural Radiance Fields (mNeRF). Both methods rely on classic Cone-Beam Computerized Tomography (CBCT); NeTT directly optimizes the CBCT densities, while the non-zero values of mNeRF are constrained by a 3D mask of the anatomic region segmented from CBCT. We demonstrate that both NeTT and mNeRF distinctly improve pose estimation within our framework. By defining a successful pose estimate to be a 3D angle error of less than 3 deg, we find that NeTT and mNeRF can achieve similar results, both with overall success rates more than 93%. However, the computational cost of NeTT is significantly lower than mNeRF in both training and pose estimation. Furthermore, we show that a NeTT trained for a single subject can generalize to synthesize high-fidelity DRRs and ensure robust pose estimations for all other subjects. Therefore, we suggest that NeTT is an attractive option for robust pose estimation using fluoroscopic projections

Limited-angle tomographic reconstruction of dense layered objects by dynamical machine learning

Limited-angle tomography of strongly scattering quasi-transparent objects is a challenging, highly ill-posed problem with practical implications in medical and biological imaging, manufacturing, automation, and environmental and food security. Regularizing priors are necessary to reduce artifacts by improving the condition of such problems. Recently, it was shown that one effective way to learn the priors for strongly scattering yet highly structured 3D objects, e.g. layered and Manhattan, is by a static neural network [Goy et al, Proc. Natl. Acad. Sci. 116, 19848-19856 (2019)]. Here, we present a radically different approach where the collection of raw images from multiple angles is viewed analogously to a dynamical system driven by the object-dependent forward scattering operator. The sequence index in angle of illumination plays the role of discrete time in the dynamical system analogy. Thus, the imaging problem turns into a problem of nonlinear system identification, which also suggests dynamical learning as better fit to regularize the reconstructions. We devised a recurrent neural network (RNN) architecture with a novel split-convolutional gated recurrent unit (SC-GRU) as the fundamental building block. Through comprehensive comparison of several quantitative metrics, we show that the dynamic method improves upon previous static approaches with fewer artifacts and better overall reconstruction fidelity.Comment: 12 pages, 7 figures, 2 table

Ultrasound Brain Tomography:Comparison of Deep Learning and Deterministic Methods

— The general purpose of this document is to develop a lightweight, portable ultrasound computer tomography (USCT) system that enables noninvasive imaging of the inside of the human head with high resolution. The goal is to analyze the benefits of using a deep neural network containing convolutional neural network (CNN) and long short-term memory (LSTM) layers compared to deterministic methods. In addition to the CNN + LSTM and LSTM networks, the following methods were used to create tomographic images of the inside of the human head: truncated singular value decomposition (TSVD), linear backprojection (LB), Gauss–Newton (GN) with regularization matrix, Tikhonov regularization (TR), and Levenberg–Marquardt (LM). A physical model of the human head was made. Based on synthetic and real measurements, images of the inside of the brain were reconstructed. On this basis, the CNN + LSTM and LSTM methods were compared with deterministic methods. Based on the comparison of images and quantitative indicators, it was found that the proposed neural network is much more tolerant of noisy and nonideal synthetic data measurements, which is manifested in the lack of the need to apply filters to the obtained images. An important finding confirmed by hard evidence is the confirmation of the greater usefulness of neural models in medical ultrasound tomography, which results from the generalization abilities of the deep hybrid neural network. At the same time, research has shown a deficit of these abilities in deterministic methods. Considering the human head’s specificity, using hybrid neural networks containing both CNN and LSTM layers in clinical trials is a better choice than deterministic methods.</p