Learned Primal-Dual Reconstruction

Anatomy-guided PET reconstruction usingl1bowsher prior

Advances in simultaneous positron emission tomography/magnetic resonance imaging (PET/MRI) technology have led to an active investigation of the anatomy-guided regularized PET image reconstruction algorithm based on MR images. Among the various priors proposed for anatomy-guided regularized PET image reconstruction, Bowsher's method based on second-order smoothing priors sometimes suffers from over-smoothing of detailed structures. Therefore, in this study, we propose a Bowsher prior based on thel1-norm and an iteratively reweighting scheme to overcome the limitation of the original Bowsher method. In addition, we have derived a closed solution for iterative image reconstruction based on this non-smooth prior. A comparison study between the originall2and proposedl1Bowsher priors was conducted using computer simulation and real human data. In the simulation and real data application, small lesions with abnormal PET uptake were better detected by the proposedl1Bowsher prior methods than the original Bowsher prior. The originall2Bowsher leads to a decreased PET intensity in small lesions when there is no clear separation between the lesions and surrounding tissue in the anatomical prior. However, the proposedl1Bowsher prior methods showed better contrast between the tumors and surrounding tissues owing to the intrinsic edge-preserving property of the prior which is attributed to the sparseness induced byl1-norm, especially in the iterative reweighting scheme. Besides, the proposed methods demonstrated lower bias and less hyper-parameter dependency on PET intensity estimation in the regions with matched anatomical boundaries in PET and MRI. Therefore, these methods will be useful for improving the PET image quality based on the anatomical side information.

Ground-truth-free deep learning for artefacts reduction in 2D radial cardiac cine MRI using a synthetically generated dataset

In this work, we consider the task of image reconstruction in 2D radial cardiac cine MRI using deep learning (DL)-based regularization. As the regularization is achieved by employing an image-prior predicted by a pre-trained convolutional neural network (CNN), the quality of the image-prior is of essential importance. The achievable performance of any DL-based method is limited by the amount and the quality of the available training data. For fast dynamic processes, obtaining good-quality MR data is challenging because of technical and physiological reasons. In this work, we try to overcome these problems by a transfer-learning approach which is motivated by a previously presented DL-method (XT,YT U-Net). There, instead of training the network on the whole 2D dynamic images, it is trained on 2D spatio-temporal profiles (xt,yt-slices) which show the temporal changes of the imaged object. Therefore, for the training and test data, it is more important that their spatio-temporal profiles share similar local features rather than being images of the same anatomy. This allows us to equip arbitrary data with simulated motion that resembles the cardiac motion and use it as training data. By doing so, it is possible to train a CNN which is applicable to cardiac cine MR data without using ground-truth cine MR images for training. We demonstrate that combining XT,YT U-Net with the proposed transfer-learning strategy delivers comparable performance to CNNs trained on cardiac cine MR images and in some cases even qualitatively surpasses these. Additionally, the transfer-learning strategy was investigated for a 2D and 3D U-Net. The images processed by the the CNNs were used as image-priors in the CNN-regularized iterative reconstruction. The XT,YT U-Net yielded visibly better results than the 2D U-Net and slightly better results than the 3D U-Net when used in combination with the presented transfer learning-strategy.

LoDoPaB-CT, a benchmark dataset for low-dose computed tomography reconstruction

Deep learning approaches for tomographic image reconstruction have become very effective and have been demonstrated to be competitive in the field. Comparing these approaches is a challenging task as they rely to a great extent on the data and setup used for training. With the Low-Dose Parallel Beam (LoDoPaB)-CT dataset, we provide a comprehensive, open-access database of computed tomography images and simulated low photon count measurements. It is suitable for training and comparing deep learning methods as well as classical reconstruction approaches. The dataset contains over 40000 scan slices from around 800 patients selected from the LIDC/IDRI database. The data selection and simulation setup are described in detail, and the generating script is publicly accessible. In addition, we provide a Python library for simplified access to the dataset and an online reconstruction challenge. Furthermore, the dataset can also be used for transfer learning as well as sparse and limited-angle reconstruction scenarios.

Measurement(s)	Low Dose Computed Tomography of the Chest • feature extraction objective
Technology Type(s)	digital curation • image processing technique
Sample Characteristic - Organism	Homo sapiens

Machine-accessible metadata file describing the reported data: 10.6084/m9.figshare.13526360

Deep learning reconstruction of digital breast tomosynthesis images for accurate breast density and patient-specific radiation dose estimation

The two-dimensional nature of mammography makes estimation of the overall breast density challenging, and estimation of the true patient-specific radiation dose impossible. Digital breast tomosynthesis (DBT), a pseudo-3D technique, is now commonly used in breast cancer screening and diagnostics. Still, the severely limited 3rd dimension information in DBT has not been used, until now, to estimate the true breast density or the patient-specific dose. This study proposes a reconstruction algorithm for DBT based on deep learning specifically optimized for these tasks. The algorithm, which we name DBToR, is based on unrolling a proximal-dual optimization method. The proximal operators are replaced with convolutional neural networks and prior knowledge is included in the model. This extends previous work on a deep learning-based reconstruction model by providing both the primal and the dual blocks with breast thickness information, which is available in DBT. Training and testing of the model were performed using virtual patient phantoms from two different sources. Reconstruction performance, and accuracy in estimation of breast density and radiation dose, were estimated, showing high accuracy (density <±3%; dose <±20%) without bias, significantly improving on the current state-of-the-art. This work also lays the groundwork for developing a deep learning-based reconstruction algorithm for the task of image interpretation by radiologists.

DIR-DBTnet: Deep iterative reconstruction network for three-dimensional digital breast tomosynthesis imaging

PURPOSE

The goal of this study is to develop a three-dimensional (3D) iterative reconstruction framework based on the deep learning (DL) technique to improve the digital breast tomosynthesis (DBT) imaging performance.

METHODS

In this work, the DIR-DBTnet is developed for DBT image reconstruction by mapping the conventional iterative reconstruction (IR) algorithm to the deep neural network. By design, the DIR-DBTnet learns and optimizes the regularizer and the iteration parameters automatically during the network training with a large amount of simulated DBT data. Numerical, experimental, and clinical data are used to evaluate its performance. Quantitative metrics such as the artifact spread function (ASF), breast density, and the signal difference to noise ratio (SDNR) are measured to assess the image quality.

RESULTS

Results show that the proposed DIR-DBTnet is able to reduce the in-plane shadow artifacts and the out-of-plane signal leaking artifacts compared to the filtered backprojection (FBP) and the total variation (TV)-based IR methods. Quantitatively, the full width half maximum (FWHM) of the measured ASF from the clinical data is 27.1% and 23.0% smaller than those obtained with the FBP and TV methods, while the SDNR is increased by 194.5% and 21.8%, respectively. In addition, the breast density obtained from the DIR-DBTnet network is more accurate and consistent with the ground truth.

CONCLUSIONS

In conclusion, a deep iterative reconstruction network, DIR-DBTnet, has been proposed for 3D DBT image reconstruction. Both qualitative and quantitative analyses of the numerical, experimental, and clinical results demonstrate that the DIR-DBTnet has superior DBT imaging performance than the conventional algorithms.

Quantitative Comparison of Deep Learning-Based Image Reconstruction Methods for Low-Dose and Sparse-Angle CT Applications

The reconstruction of computed tomography (CT) images is an active area of research. Following the rise of deep learning methods, many data-driven models have been proposed in recent years. In this work, we present the results of a data challenge that we organized, bringing together algorithm experts from different institutes to jointly work on quantitative evaluation of several data-driven methods on two large, public datasets during a ten day sprint. We focus on two applications of CT, namely, low-dose CT and sparse-angle CT. This enables us to fairly compare different methods using standardized settings. As a general result, we observe that the deep learning-based methods are able to improve the reconstruction quality metrics in both CT applications while the top performing methods show only minor differences in terms of peak signal-to-noise ratio (PSNR) and structural similarity (SSIM). We further discuss a number of other important criteria that should be taken into account when selecting a method, such as the availability of training data, the knowledge of the physical measurement model and the reconstruction speed.

Accelerated 3D image reconstruction with a morphological pyramid and noise-power convergence criterion

Model-based iterative reconstruction (MBIR) for cone-beam CT (CBCT) offers better noise-resolution tradeoff and image quality than analytical methods for acquisition protocols with low x-ray dose or limited data, but with increased computational burden that poses a drawback to routine application in clinical scenarios. This work develops a comprehensive framework for acceleration of MBIR in the form of penalized weighted least squares optimized with ordered subsets separable quadratic surrogates. The optimization was scheduled on a set of stages forming a morphological pyramid varying in voxel size. Transition between stages was controlled with a convergence criterion based on the deviation between the mid-band noise power spectrum (NPS) measured on a homogeneous region of the evolving reconstruction and that expected for the converged image, computed with an analytical model that used projection data and the reconstruction parameters. A stochastic backprojector was developed by introducing a random perturbation to the sampling position of each voxel for each ray in the reconstruction within a voxel-based backprojector, breaking the deterministic pattern of sampling artifacts when combined with an unmatched Siddon forward projector. This fast, forward and backprojector pair were included into a multi-resolution reconstruction strategy to provide support for objects partially outside of the field of view. Acceleration from ordered subsets was combined with momentum accumulation stabilized with an adaptive technique that automatically resets the accumulated momentum when it diverges noticeably from the current iteration update. The framework was evaluated with CBCT data of a realistic abdomen phantom acquired on an imaging x-ray bench and with clinical CBCT data from an angiography robotic C-arm (Artis Zeego, Siemens Healthineers, Forchheim, Germany) acquired during a liver embolization procedure. Image fidelity was assessed with the structural similarity index (SSIM) computed with a converged reconstruction. The accelerated framework provided accurate reconstructions in 60 s (SSIM = 0.97) and as little as 27 s (SSIM = 0.94) for soft-tissue evaluation. The use of simple forward and backprojectors resulted in 9.3× acceleration. Accumulation of momentum provided extra ∼3.5× acceleration with stable convergence for 6-30 subsets. The NPS-driven morphological pyramid resulted in initial faster convergence, achieving similar SSIM with 1.5× lower runtime than the single-stage optimization. Acceleration of MBIR to provide reconstruction time compatible with clinical applications is feasible via architectures that integrate algorithmic acceleration with approaches to provide stable convergence, and optimization schedules that maximize convergence speed.

MetaInv-Net: Meta Inversion Network for Sparse View CT Image Reconstruction

X-ray Computed Tomography (CT) is widely used in clinical applications such as diagnosis and image-guided interventions. In this paper, we propose a new deep learning based model for CT image reconstruction with the backbone network architecture built by unrolling an iterative algorithm. However, unlike the existing strategy to include as many data-adaptive components in the unrolled dynamics model as possible, we find that it is enough to only learn the parts where traditional designs mostly rely on intuitions and experience. More specifically, we propose to learn an initializer for the conjugate gradient (CG) algorithm that involved in one of the subproblems of the backbone model. Other components, such as image priors and hyperparameters, are kept as the original design. Since a hypernetwork is introduced to inference on the initialization of the CG module, it makes the proposed model a certain meta-learning model. Therefore, we shall call the proposed model the meta-inversion network (MetaInv-Net). The proposed MetaInv-Net can be designed with much less trainable parameters while still preserves its superior image reconstruction performance than some state-of-the-art deep models in CT imaging. In simulated and real data experiments, MetaInv-Net performs very well and can be generalized beyond the training setting, i.e., to other scanning settings, noise levels, and data sets.

Electrical Properties Tomography: A Methodological Review

Electrical properties tomography (EPT) is an imaging method that uses a magnetic resonance (MR) system to non-invasively determine the spatial distribution of the conductivity and permittivity of the imaged object. This manuscript starts by providing clear definitions about the data required for, and acquired in, EPT, followed by comprehensively formulating the physical equations underlying a large number of analytical EPT techniques. This thorough mathematical overview of EPT harmonizes several EPT techniques in a single type of formulation and gives insight into how they act on the data and what their data requirements are. Furthermore, the review describes machine learning-based algorithms. Matlab code of several differential and iterative integral methods is available upon request.

On Learned Operator Correction in Inverse Problems

We discuss the possibility of learning a data-driven explicit model correction for inverse problems and whether such a model correction can be used within a variational framework to obtain regularized reconstructions. This paper discusses the conceptual difficulty of learning such a forward model correction and proceeds to present a possible solution as a forward-adjoint correction that explicitly corrects in both data and solution spaces. We then derive conditions under which solutions to the variational problem with a learned correction converge to solutions obtained with the correct operator. The proposed approach is evaluated on an application to limited view photoacoustic tomography and compared to the established framework of the Bayesian approximation error method.

Exploiting prior knowledge about biological macromolecules in cryo-EM structure determination

Three-dimensional reconstruction of the electron-scattering potential of biological macromolecules from electron cryo-microscopy (cryo-EM) projection images is an ill-posed problem. The most popular cryo-EM software solutions to date rely on a regularization approach that is based on the prior assumption that the scattering potential varies smoothly over three-dimensional space. Although this approach has been hugely successful in recent years, the amount of prior knowledge that it exploits compares unfavorably with the knowledge about biological structures that has been accumulated over decades of research in structural biology. Here, a regularization framework for cryo-EM structure determination is presented that exploits prior knowledge about biological structures through a convolutional neural network that is trained on known macromolecular structures. This neural network is inserted into the iterative cryo-EM structure-determination process through an approach that is inspired by regularization by denoising. It is shown that the new regularization approach yields better reconstructions than the current state of the art for simulated data, and options to extend this work for application to experimental cryo-EM data are discussed.

AMP-Net: Denoising-Based Deep Unfolding for Compressive Image Sensing

Most compressive sensing (CS) reconstruction methods can be divided into two categories, i.e. model-based methods and classical deep network methods. By unfolding the iterative optimization algorithm for model-based methods onto networks, deep unfolding methods have the good interpretation of model-based methods and the high speed of classical deep network methods. In this article, to solve the visual image CS problem, we propose a deep unfolding model dubbed AMP-Net. Rather than learning regularization terms, it is established by unfolding the iterative denoising process of the well-known approximate message passing algorithm. Furthermore, AMP-Net integrates deblocking modules in order to eliminate the blocking artifacts that usually appear in CS of visual images. In addition, the sampling matrix is jointly trained with other network parameters to enhance the reconstruction performance. Experimental results show that the proposed AMP-Net has better reconstruction accuracy than other state-of-the-art methods with high reconstruction speed and a small number of network parameters.

Alternating Primal-Dual Algorithm for Minimizing Multiple-Summed Separable Problems with Application to Image Restoration

In order to discover the difference among dual strategies, we propose an alternating primal-dual algorithm (APDA) that can be considered as a general version for minimizing problem which is multiple-summed separable convex but not necessarily smooth. First, the original multiple-summed problem is transformed into two subproblems. Second, one subproblem is solved in the primal space and the other is solved in the dual space. Finally, the alternating direction method is executed between the primal and the dual part. Furthermore, the classical alternating direction method of multipliers (ADMM) is extended to solve the primal subproblem which is also multiple summed, therefore, the extended ADMM can be seen as a parallel method for the original problem. Thanks to the flexibility of APDA, different dual strategies for image restoration are analyzed. Numerical experiments show that the proposed method performs better than some existing algorithms in terms of both speed and accuracy.

A Computationally Efficient Reconstruction Algorithm for Circular Cone-Beam Computed Tomography Using Shallow Neural Networks

Circular cone-beam (CCB) Computed Tomography (CT) has become an integral part of industrial quality control, materials science and medical imaging. The need to acquire and process each scan in a short time naturally leads to trade-offs between speed and reconstruction quality, creating a need for fast reconstruction algorithms capable of creating accurate reconstructions from limited data. In this paper, we introduce the Neural Network Feldkamp-Davis-Kress (NN-FDK) algorithm. This algorithm adds a machine learning component to the FDK algorithm to improve its reconstruction accuracy while maintaining its computational efficiency. Moreover, the NN-FDK algorithm is designed such that it has low training data requirements and is fast to train. This ensures that the proposed algorithm can be used to improve image quality in high-throughput CT scanning settings, where FDK is currently used to keep pace with the acquisition speed using readily available computational resources. We compare the NN-FDK algorithm to two standard CT reconstruction algorithms and to two popular deep neural networks trained to remove reconstruction artifacts from the 2D slices of an FDK reconstruction. We show that the NN-FDK reconstruction algorithm is substantially faster in computing a reconstruction than all the tested alternative methods except for the standard FDK algorithm and we show it can compute accurate CCB CT reconstructions in cases of high noise, a low number of projection angles or large cone angles. Moreover, we show that the training time of an NN-FDK network is orders of magnitude lower than the considered deep neural networks, with only a slight reduction in reconstruction accuracy.

Sparse-view CT reconstruction based on multi-level wavelet convolution neural network

Sparse-view computed tomography (CT) is a recent approach to reducing the radiation dose in patients and speeding up the data acquisition. Consequently, sparse-view CT has been of particular interest among researchers within the CT community. Advanced reconstruction algorithms for sparse-view CT, such as iterative algorithms with total-variation (TV), have been studied along with the problem of increasing computational burden and the blurring of artifacts in the reconstructed images. Studies on deep-learning-based approaches applying U-NET have recently achieved remarkable outcomes in various domains including low-dose CT. In this study, we propose a new method for sparse-view CT reconstruction based on a multi-level wavelet convolutional neural network (MWCNN). First, a filtered backprojection (FBP) was used to reconstruct a sparsely sampled sinogram from 60, 120, and 180 projections. Subsequently, the sparse-view data obtained from FBP were fed to a deep-learning network, i.e., the MWCNN. Our network architecture combines a wavelet transform and modified U-NET without pooling. By replacing the pooling function with the wavelet transform, the receptive field is enlarged to improve the performance. We qualitatively and quantitatively evaluated the interpolation, iterative TV method, and standard U-NET in terms of a reduction in the streaking artifacts and a preservation of the anatomical structures. When compared with other methods, the proposed method showed the highest performance based on various evaluation parameters such as the structural similarity, root mean square error, and resolution. These results indicate that the MWCNN possesses a powerful potential for achieving a sparse-view CT reconstruction.

Advancing machine learning for MR image reconstruction with an open competition: Overview of the 2019 fastMRI challenge

PURPOSE

To advance research in the field of machine learning for MR image reconstruction with an open challenge.

METHODS

We provided participants with a dataset of raw k-space data from 1,594 consecutive clinical exams of the knee. The goal of the challenge was to reconstruct images from these data. In order to strike a balance between realistic data and a shallow learning curve for those not already familiar with MR image reconstruction, we ran multiple tracks for multi-coil and single-coil data. We performed a two-stage evaluation based on quantitative image metrics followed by evaluation by a panel of radiologists. The challenge ran from June to December of 2019.

RESULTS

We received a total of 33 challenge submissions. All participants chose to submit results from supervised machine learning approaches.

CONCLUSIONS

The challenge led to new developments in machine learning for image reconstruction, provided insight into the current state of the art in the field, and highlighted remaining hurdles for clinical adoption.

Known Operator Learning Enables Constrained Projection Geometry Conversion: Parallel to Cone-Beam for Hybrid MR/X-Ray Imaging

X-ray imaging is a wide-spread real-time imaging technique. Magnetic Resonance Imaging (MRI) offers a multitude of contrasts that offer improved guidance to interventionalists. As such simultaneous real-time acquisition and overlay would be highly favorable for image-guided interventions, e.g., in stroke therapy. One major obstacle in this setting is the fundamentally different acquisition geometry. MRI k -space sampling is associated with parallel projection geometry, while the X-ray acquisition results in perspective distorted projections. The classical rebinning methods to overcome this limitation inherently suffers from a loss of resolution. To counter this problem, we present a novel rebinning algorithm for parallel to cone-beam conversion. We derive a rebinning formula that is then used to find an appropriate deep neural network architecture. Following the known operator learning paradigm, the novel algorithm is mapped to a neural network with differentiable projection operators enabling data-driven learning of the remaining unknown operators. The evaluation aims in two directions: First, we give a profound analysis of the different hypotheses to the unknown operator and investigate the influence of numerical training data. Second, we evaluate the performance of the proposed method against the classical rebinning approach. We demonstrate that the derived network achieves better results than the baseline method and that such operators can be trained with simulated data without losing their generality making them applicable to real data without the need for retraining or transfer learning.

Learned Proximal Networks for Quantitative Susceptibility Mapping

Quantitative Susceptibility Mapping (QSM) estimates tissue magnetic susceptibility distributions from Magnetic Resonance (MR) phase measurements by solving an ill-posed dipole inversion problem. Conventional single orientation QSM methods usually employ regularization strategies to stabilize such inversion, but may suffer from streaking artifacts or over-smoothing. Multiple orientation QSM such as calculation of susceptibility through multiple orientation sampling (COSMOS) can give well-conditioned inversion and an artifact free solution but has expensive acquisition costs. On the other hand, Convolutional Neural Networks (CNN) show great potential for medical image reconstruction, albeit often with limited interpretability. Here, we present a Learned Proximal Convolutional Neural Network (LP-CNN) for solving the ill-posed QSM dipole inversion problem in an iterative proximal gradient descent fashion. This approach combines the strengths of data-driven restoration priors and the clear interpretability of iterative solvers that can take into account the physical model of dipole convolution. During training, our LP-CNN learns an implicit regularizer via its proximal, enabling the decoupling between the forward operator and the data-driven parameters in the reconstruction algorithm. More importantly, this framework is believed to be the first deep learning QSM approach that can naturally handle an arbitrary number of phase input measurements without the need for any ad-hoc rotation or re-training. We demonstrate that the LP-CNN provides state-of-the-art reconstruction results compared to both traditional and deep learning methods while allowing for more flexibility in the reconstruction process.

Dense Recurrent Neural Networks for Accelerated MRI: History-Cognizant Unrolling of Optimization Algorithms

Inverse problems for accelerated MRI typically incorporate domain-specific knowledge about the forward encoding operator in a regularized reconstruction framework. Recently physics-driven deep learning (DL) methods have been proposed to use neural networks for data-driven regularization. These methods unroll iterative optimization algorithms to solve the inverse problem objective function, by alternating between domain-specific data consistency and data-driven regularization via neural networks. The whole unrolled network is then trained end-to-end to learn the parameters of the network. Due to simplicity of data consistency updates with gradient descent steps, proximal gradient descent (PGD) is a common approach to unroll physics-driven DL reconstruction methods. However, PGD methods have slow convergence rates, necessitating a higher number of unrolled iterations, leading to memory issues in training and slower reconstruction times in testing. Inspired by efficient variants of PGD methods that use a history of the previous iterates, we propose a history-cognizant unrolling of the optimization algorithm with dense connections across iterations for improved performance. In our approach, the gradient descent steps are calculated at a trainable combination of the outputs of all the previous regularization units. We also apply this idea to unrolling variable splitting methods with quadratic relaxation. Our results in reconstruction of the fastMRI knee dataset show that the proposed history-cognizant approach reduces residual aliasing artifacts compared to its conventional unrolled counterpart without requiring extra computational power or increasing reconstruction time.

Adaptive and Compressive Beamforming Using Deep Learning for Medical Ultrasound

In ultrasound (US) imaging, various types of adaptive beamforming techniques have been investigated to improve the resolution and the contrast-to-noise ratio of the delay and sum (DAS) beamformers. Unfortunately, the performance of these adaptive beamforming approaches degrades when the underlying model is not sufficiently accurate and the number of channels decreases. To address this problem, here, we propose a deep-learning-based beamformer to generate significantly improved images over widely varying measurement conditions and channel subsampling patterns. In particular, our deep neural network is designed to directly process full or subsampled radio frequency (RF) data acquired at various subsampling rates and detector configurations so that it can generate high-quality US images using a single beamformer. The origin of such input-dependent adaptivity is also theoretically analyzed. Experimental results using the B-mode focused US confirm the efficacy of the proposed methods.

Neural networks-based regularization for large-scale medical image reconstruction

In this paper we present a generalized Deep Learning-based approach for solving ill-posed large-scale inverse problems occuring in medical image reconstruction. Recently, Deep Learning methods using iterative neural networks (NNs) and cascaded NNs have been reported to achieve state-of-the-art results with respect to various quantitative quality measures as PSNR, NRMSE and SSIM across different imaging modalities. However, the fact that these approaches employ the application of the forward and adjoint operators repeatedly in the network architecture requires the network to process the whole images or volumes at once, which for some applications is computationally infeasible. In this work, we follow a different reconstruction strategy by strictly separating the application of the NN, the regularization of the solution and the consistency with the measured data. The regularization is given in the form of an image prior obtained by the output of a previously trained NN which is used in a Tikhonov regularization framework. By doing so, more complex and sophisticated network architectures can be used for the removal of the artefacts or noise than it is usually the case in iterative NNs. Due to the large scale of the considered problems and the resulting computational complexity of the employed networks, the priors are obtained by processing the images or volumes as patches or slices. We evaluated the method for the cases of 3D cone-beam low dose CT and undersampled 2D radial cine MRI and compared it to a total variation-minimization-based reconstruction algorithm as well as to a method with regularization based on learned overcomplete dictionaries. The proposed method outperformed all the reported methods with respect to all chosen quantitative measures and further accelerates the regularization step in the reconstruction by several orders of magnitude.

SACNN: Self-Attention Convolutional Neural Network for Low-Dose CT Denoising With Self-Supervised Perceptual Loss Network

Computed tomography (CT) is a widely used screening and diagnostic tool that allows clinicians to obtain a high-resolution, volumetric image of internal structures in a non-invasive manner. Increasingly, efforts have been made to improve the image quality of low-dose CT (LDCT) to reduce the cumulative radiation exposure of patients undergoing routine screening exams. The resurgence of deep learning has yielded a new approach for noise reduction by training a deep multi-layer convolutional neural networks (CNN) to map the low-dose to normal-dose CT images. However, CNN-based methods heavily rely on convolutional kernels, which use fixed-size filters to process one local neighborhood within the receptive field at a time. As a result, they are not efficient at retrieving structural information across large regions. In this paper, we propose a novel 3D self-attention convolutional neural network for the LDCT denoising problem. Our 3D self-attention module leverages the 3D volume of CT images to capture a wide range of spatial information both within CT slices and between CT slices. With the help of the 3D self-attention module, CNNs are able to leverage pixels with stronger relationships regardless of their distance and achieve better denoising results. In addition, we propose a self-supervised learning scheme to train a domain-specific autoencoder as the perceptual loss function. We combine these two methods and demonstrate their effectiveness on both CNN-based neural networks and WGAN-based neural networks with comprehensive experiments. Tested on the AAPM-Mayo Clinic Low Dose CT Grand Challenge data set, our experiments demonstrate that self-attention (SA) module and autoencoder (AE) perceptual loss function can efficiently enhance traditional CNNs and can achieve comparable or better results than the state-of-the-art methods.

Low-dose CT with deep learning regularization via proximal forward-backward splitting

Low-dose x-ray computed tomography (LDCT) is desirable for reduced patient dose. This work develops new image reconstruction methods with deep learning (DL) regularization for LDCT. Our methods are based on the unrolling of a proximal forward-backward splitting (PFBS) framework with data-driven image regularization via deep neural networks. In contrast to PFBS-IR, which utilizes standard data fidelity updates via an iterative reconstruction (IR) method, PFBS-AIR involves preconditioned data fidelity updates that fuse the analytical reconstruction (AR) and IR methods in a synergistic way, i.e. fused analytical and iterative reconstruction (AIR). The results suggest that the DL-regularized methods (PFBS-IR and PFBS-AIR) provide better reconstruction quality compared to conventional methods (AR or IR). In addition, owing to the AIR, PFBS-AIR noticeably outperformed PFBS-IR and another DL-based postprocessing method, FBPConvNet.

High-dimensional embedding network derived prior for compressive sensing MRI reconstruction

Although recent deep learning methodology has shown promising performance in fast imaging, the network needs to be retrained for specific sampling patterns and ratios. Therefore, how to explore the network as a general prior and leverage it into the observation constraint flexibly is urgent. In this work, we present a multi-channel enhanced Deep Mean-Shift Prior (MEDMSP) to address the highly under-sampled magnetic resonance imaging reconstruction problem. By extending the naive DMSP via integration of multi-model aggregation and multi-channel network learning, a high-dimensional embedding network derived prior is formed. Then, we apply the learned prior to single-channel image reconstruction via variable augmentation technique. The resulting model is tackled by proximal gradient descent and alternative iteration. Experimental results under various sampling trajectories and acceleration factors consistently demonstrated the superiority of the proposed prior.

Radon Inversion via Deep Learning

The Radon transform is widely used in physical and life sciences, and one of its major applications is in medical X-ray computed tomography (CT), which is significantly important in disease screening and diagnosis. In this paper, we propose a novel reconstruction framework for Radon inversion with deep learning (DL) techniques. For simplicity, the proposed framework is denoted as iRadonMAP, i.e., inverse Radon transform approximation. Specifically, we construct an interpretable neural network that contains three dedicated components. The first component is a fully connected filtering (FCF) layer along the rotation angle direction in the sinogram domain, and the second one is a sinusoidal back-projection (SBP) layer, which back-projects the filtered sinogram data into the spatial domain. Next, a common network structure is added to further improve the overall performance. iRadonMAP is first pretrained on a large number of generic images from the ImageNet database and then fine-tuned with clinical patient data. The experimental results demonstrate the feasibility of the proposed iRadonMAP framework for Radon inversion.

Multi-Modal Deep Guided Filtering for Comprehensible Medical Image Processing

Deep learning-based image processing is capable of creating highly appealing results. However, it is still widely considered as a "blackbox" transformation. In medical imaging, this lack of comprehensibility of the results is a sensitive issue. The integration of known operators into the deep learning environment has proven to be advantageous for the comprehensibility and reliability of the computations. Consequently, we propose the use of the locally linear guided filter in combination with a learned guidance map for general purpose medical image processing. The output images are only processed by the guided filter while the guidance map can be trained to be task-optimal in an end-to-end fashion. We investigate the performance based on two popular tasks: image super resolution and denoising. The evaluation is conducted based on pairs of multi-modal magnetic resonance imaging and cross-modal computed tomography and magnetic resonance imaging datasets. For both tasks, the proposed approach is on par with state-of-the-art approaches. Additionally, we can show that the input image's content is almost unchanged after the processing which is not the case for conventional deep learning approaches. On top, the proposed pipeline offers increased robustness against degraded input as well as adversarial attacks.

DirectPET: full-size neural network PET reconstruction from sinogram data

Purpose: Neural network image reconstruction directly from measurement data is a relatively new field of research, which until now has been limited to producing small single-slice images (e.g., 1 × 128 × 128 ). We proposed a more efficient network design for positron emission tomography called DirectPET, which is capable of reconstructing multislice image volumes (i.e., 16 × 400 × 400 ) from sinograms. Approach: Large-scale direct neural network reconstruction is accomplished by addressing the associated memory space challenge through the introduction of a specially designed Radon inversion layer. Using patient data, we compare the proposed method to the benchmark ordered subsets expectation maximization (OSEM) algorithm using signal-to-noise ratio, bias, mean absolute error, and structural similarity measures. In addition, line profiles and full-width half-maximum measurements are provided for a sample of lesions. Results: DirectPET is shown capable of producing images that are quantitatively and qualitatively similar to the OSEM target images in a fraction of the time. We also report on an experiment where DirectPET is trained to map low-count raw data to normal count target images, demonstrating the method's ability to maintain image quality under a low-dose scenario. Conclusion: The ability of DirectPET to quickly reconstruct high-quality, multislice image volumes suggests potential clinical viability of the method. However, design parameters and performance boundaries need to be fully established before adoption can be considered.

Multi-Scale Learned Iterative Reconstruction

Model-based learned iterative reconstruction methods have recently been shown to outperform classical reconstruction algorithms. Applicability of these methods to large scale inverse problems is however limited by the available memory for training and extensive training times, the latter due to computationally expensive forward models. As a possible solution to these restrictions we propose a multi-scale learned iterative reconstruction scheme that computes iterates on discretisations of increasing resolution. This procedure does not only reduce memory requirements, it also considerably speeds up reconstruction and training times, but most importantly is scalable to large scale inverse problems with non-trivial forward operators, such as those that arise in many 3D tomographic applications. In particular, we propose a hybrid network that combines the multiscale iterative approach with a particularly expressive network architecture which in combination exhibits excellent scalability in 3D. Applicability of the algorithm is demonstrated for 3D cone beam computed tomography from real measurement data of an organic phantom. Additionally, we examine scalability and reconstruction quality in comparison to established learned reconstruction methods in two dimensions for low dose computed tomography on human phantoms.

MoDL-MUSSELS: Model-Based Deep Learning for Multishot Sensitivity-Encoded Diffusion MRI

We introduce a model-based deep learning architecture termed MoDL-MUSSELS for the correction of phase errors in multishot diffusion-weighted echo-planar MR images. The proposed algorithm is a generalization of the existing MUSSELS algorithm with similar performance but significantly reduced computational complexity. In this work, we show that an iterative re-weighted least-squares implementation of MUSSELS alternates between a multichannel filter bank and the enforcement of data consistency. The multichannel filter bank projects the data to the signal subspace, thus exploiting the annihilation relations between shots. Due to the high computational complexity of the self-learned filter bank, we propose replacing it with a convolutional neural network (CNN) whose parameters are learned from exemplary data. The proposed CNN is a hybrid model involving a multichannel CNN in the k-space and another CNN in the image space. The k-space CNN exploits the annihilation relations between the shot images, while the image domain network is used to project the data to an image manifold. The experiments show that the proposed scheme can yield reconstructions that are comparable to state-of-the-art methods while offering several orders of magnitude reduction in run-time.

Benchmarking MRI Reconstruction Neural Networks on Large Public Datasets

Deep learning is starting to offer promising results for reconstruction in Magnetic Resonance Imaging (MRI). A lot of networks are being developed, but the comparisons remain hard because the frameworks used are not the same among studies, the networks are not properly re-trained, and the datasets used are not the same among comparisons. The recent release of a public dataset, fastMRI, consisting of raw k-space data, encouraged us to write a consistent benchmark of several deep neural networks for MR image reconstruction. This paper shows the results obtained for this benchmark, allowing to compare the networks, and links the open source implementation of all these networks in Keras. The main finding of this benchmark is that it is beneficial to perform more iterations between the image and the measurement spaces compared to having a deeper per-space network.

Spatio-Temporal Deep Learning-Based Undersampling Artefact Reduction for 2D Radial Cine MRI With Limited Training Data

In this work we reduce undersampling artefacts in two-dimensional (2D) golden-angle radial cine cardiac MRI by applying a modified version of the U-net. The network is trained on 2D spatio-temporal slices which are previously extracted from the image sequences. We compare our approach to two 2D and a 3D deep learning-based post processing methods, three iterative reconstruction methods and two recently proposed methods for dynamic cardiac MRI based on 2D and 3D cascaded networks. Our method outperforms the 2D spatially trained U-net and the 2D spatio-temporal U-net. Compared to the 3D spatio-temporal U-net, our method delivers comparable results, but requiring shorter training times and less training data. Compared to the compressed sensing-based methods kt-FOCUSS and a total variation regularized reconstruction approach, our method improves image quality with respect to all reported metrics. Further, it achieves competitive results when compared to the iterative reconstruction method based on adaptive regularization with dictionary learning and total variation and when compared to the methods based on cascaded networks, while only requiring a small fraction of the computational and training time. A persistent homology analysis demonstrates that the data manifold of the spatio-temporal domain has a lower complexity than the one of the spatial domain and therefore, the learning of a projection-like mapping is facilitated. Even when trained on only one single subject without data-augmentation, our approach yields results which are similar to the ones obtained on a large training dataset. This makes the method particularly suitable for training a network on limited training data. Finally, in contrast to the spatial 2D U-net, our proposed method is shown to be naturally robust with respect to image rotation in image space and almost achieves rotation-equivariance where neither data-augmentation nor a particular network design are required.

SPULTRA: Low-Dose CT Image Reconstruction With Joint Statistical and Learned Image Models

Low-dose CT image reconstruction has been a popular research topic in recent years. A typical reconstruction method based on post-log measurements is called penalized weighted-least squares (PWLS). Due to the underlying limitations of the post-log statistical model, the PWLS reconstruction quality is often degraded in low-dose scans. This paper investigates a shifted-Poisson (SP) model based likelihood function that uses the pre-log raw measurements that better represents the measurement statistics, together with a data-driven regularizer exploiting a Union of Learned TRAnsforms (SPULTRA). Both the SP induced data-fidelity term and the regularizer in the proposed framework are nonconvex. The proposed SPULTRA algorithm uses quadratic surrogate functions for the SP induced data-fidelity term. Each iteration involves a quadratic subproblem for updating the image, and a sparse coding and clustering subproblem that has a closed-form solution. The SPULTRA algorithm has a similar computational cost per iteration as its recent counterpart PWLS-ULTRA that uses post-log measurements, and it provides better image reconstruction quality than PWLS-ULTRA, especially in low-dose scans.

ADMM-CSNet: A Deep Learning Approach for Image Compressive Sensing

Compressive sensing (CS) is an effective technique for reconstructing image from a small amount of sampled data. It has been widely applied in medical imaging, remote sensing, image compression, etc. In this paper, we propose two versions of a novel deep learning architecture, dubbed as ADMM-CSNet, by combining the traditional model-based CS method and data-driven deep learning method for image reconstruction from sparsely sampled measurements. We first consider a generalized CS model for image reconstruction with undetermined regularizations in undetermined transform domains, and then two efficient solvers using Alternating Direction Method of Multipliers (ADMM) algorithm for optimizing the model are proposed. We further unroll and generalize the ADMM algorithm to be two deep architectures, in which all parameters of the CS model and the ADMM algorithm are discriminatively learned by end-to-end training. For both applications of fast CS complex-valued MR imaging and CS imaging of real-valued natural images, the proposed ADMM-CSNet achieved favorable reconstruction accuracy in fast computational speed compared with the traditional and the other deep learning methods.

Accelerating MR Imaging via Deep Chambolle-Pock Network

Compressed sensing (CS) has been introduced to accelerate data acquisition in MR Imaging. However, CS-MRI methods suffer from detail loss with large acceleration and complicated parameter selection. To address the limitations of existing CS-MRI methods, a model-driven MR reconstruction is proposed that trains a deep network, named CP-net, which is derived from the Chambolle-Pock algorithm to reconstruct the in vivo MR images of human brains from highly undersampled complex k-space data acquired on different types of MR scanners. The proposed deep network can learn the proximal operator and parameters among the Chambolle-Pock algorithm. All of the experiments show that the proposed CP-net achieves more accurate MR reconstruction results, outperforming state-of-the-art methods across various quantitative metrics.

Deep Magnetic Resonance Image Reconstruction: Inverse Problems Meet Neural Networks

Image reconstruction from undersampled k-space data has been playing an important role in fast MRI. Recently, deep learning has demonstrated tremendous success in various fields and has also shown potential in significantly accelerating MRI reconstruction with fewer measurements. This article provides an overview of the deep learning-based image reconstruction methods for MRI. Two types of deep learning-based approaches are reviewed: those based on unrolled algorithms and those which are not. The main structure of both approaches are explained, respectively. Several signal processing issues for maximizing the potential of deep reconstruction in fast MRI are discussed. The discussion may facilitate further development of the networks and the analysis of performance from a theoretical point of view.

A Partially-Learned Algorithm for Joint Photo-acoustic Reconstruction and Segmentation

In an inhomogeneously illuminated photoacoustic image, important information like vascular geometry is not readily available, when only the initial pressure is reconstructed. To obtain the desired information, algorithms for image segmentation are often applied as a post-processing step. In this article, we propose to jointly acquire the photoacoustic reconstruction and segmentation, by modifying a recently developed partially learned algorithm based on a convolutional neural network. We investigate the stability of the algorithm against changes in initial pressures and photoacoustic system settings. These insights are used to develop an algorithm that is robust to input and system settings. Our approach can easily be applied to other imaging modalities and can be modified to perform other high-level tasks different from segmentation. The method is validated on challenging synthetic and experimental photoacoustic tomography data in limited angle and limited view scenarios. It is computationally less expensive than classical iterative methods and enables higher quality reconstructions and segmentations than the state-of-the-art learned and non-learned methods.

Image Reconstruction: From Sparsity to Data-adaptive Methods and Machine Learning

The field of medical image reconstruction has seen roughly four types of methods. The first type tended to be analytical methods, such as filtered back-projection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform for magnetic resonance imaging (MRI), based on simple mathematical models for the imaging systems. These methods are typically fast, but have suboptimal properties such as poor resolution-noise trade-off for CT. A second type is iterative reconstruction methods based on more complete models for the imaging system physics and, where appropriate, models for the sensor statistics. These iterative methods improved image quality by reducing noise and artifacts. The FDA-approved methods among these have been based on relatively simple regularization models. A third type of methods has been designed to accommodate modified data acquisition methods, such as reduced sampling in MRI and CT to reduce scan time or radiation dose. These methods typically involve mathematical image models involving assumptions such as sparsity or low-rank. A fourth type of methods replaces mathematically designed models of signals and systems with data-driven or adaptive models inspired by the field of machine learning. This paper focuses on the two most recent trends in medical image reconstruction: methods based on sparsity or low-rank models, and data-driven methods based on machine learning techniques.

CT Super-Resolution GAN Constrained by the Identical, Residual, and Cycle Learning Ensemble (GAN-CIRCLE)

In this paper, we present a semi-supervised deep learning approach to accurately recover high-resolution (HR) CT images from low-resolution (LR) counterparts. Specifically, with the generative adversarial network (GAN) as the building block, we enforce the cycle-consistency in terms of the Wasserstein distance to establish a nonlinear end-to-end mapping from noisy LR input images to denoised and deblurred HR outputs. We also include the joint constraints in the loss function to facilitate structural preservation. In this process, we incorporate deep convolutional neural network (CNN), residual learning, and network in network techniques for feature extraction and restoration. In contrast to the current trend of increasing network depth and complexity to boost the imaging performance, we apply a parallel 1×1 CNN to compress the output of the hidden layer and optimize the number of layers and the number of filters for each convolutional layer. The quantitative and qualitative evaluative results demonstrate that our proposed model is accurate, efficient and robust for super-resolution (SR) image restoration from noisy LR input images. In particular, we validate our composite SR networks on three large-scale CT datasets, and obtain promising results as compared to the other state-of-the-art methods.

A Convex Variational Model for Learning Convolutional Image Atoms from Incomplete Data

A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is convex and allows for simultaneous image reconstruction and atom learning in a general, inverse problems context. Further, motivated by an improved numerical performance, also a semi-convex variant is included in the analysis and the experiments of the paper. For both settings, fundamental analytical properties allowing in particular to ensure well-posedness and stability results for inverse problems are proven in a continuous setting. Exploiting convexity, globally optimal solutions are further computed numerically for applications with incomplete, noisy and blurry data and numerical results are shown.

Convolutional Sparse Coding for Compressed Sensing CT Reconstruction

Over the past few years, dictionary learning (DL)-based methods have been successfully used in various image reconstruction problems. However, the traditional DL-based computed tomography (CT) reconstruction methods are patch-based and ignore the consistency of pixels in overlapped patches. In addition, the features learned by these methods always contain shifted versions of the same features. In recent years, convolutional sparse coding (CSC) has been developed to address these problems. In this paper, inspired by several successful applications of CSC in the field of signal processing, we explore the potential of CSC in sparse-view CT reconstruction. By directly working on the whole image, without the necessity of dividing the image into overlapped patches in DL-based methods, the proposed methods can maintain more details and avoid artifacts caused by patch aggregation. With predetermined filters, an alternating scheme is developed to optimize the objective function. Extensive experiments with simulated and real CT data were performed to validate the effectiveness of the proposed methods. The qualitative and quantitative results demonstrate that the proposed methods achieve better performance than the several existing state-of-the-art methods.

Technical Note: PYRO-NN: Python reconstruction operators in neural networks

PURPOSE

Recently, several attempts were conducted to transfer deep learning to medical image reconstruction. An increasingly number of publications follow the concept of embedding the computed tomography (CT) reconstruction as a known operator into a neural network. However, most of the approaches presented lack an efficient CT reconstruction framework fully integrated into deep learning environments. As a result, many approaches use workarounds for mathematically unambiguously solvable problems.

METHODS

PYRO-NN is a generalized framework to embed known operators into the prevalent deep learning framework Tensorflow. The current status includes state-of-the-art parallel-, fan-, and cone-beam projectors, and back-projectors accelerated with CUDA provided as Tensorflow layers. On top, the framework provides a high-level Python API to conduct FBP and iterative reconstruction experiments with data from real CT systems.

RESULTS

The framework provides all necessary algorithms and tools to design end-to-end neural network pipelines with integrated CT reconstruction algorithms. The high-level Python API allows a simple use of the layers as known from Tensorflow. All algorithms and tools are referenced to a scientific publication and are compared to existing non-deep learning reconstruction frameworks. To demonstrate the capabilities of the layers, the framework comes with baseline experiments, which are described in the supplementary material. The framework is available as open-source software under the Apache 2.0 licence at https://github.com/csyben/PYRO-NN.

CONCLUSIONS

PYRO-NN comes with the prevalent deep learning framework Tensorflow and allows to setup end-to-end trainable neural networks in the medical image reconstruction context. We believe that the framework will be a step toward reproducible research and give the medical physics community a toolkit to elevate medical image reconstruction with new deep learning techniques.

Network Accelerated Motion Estimation and Reduction (NAMER): Convolutional neural network guided retrospective motion correction using a separable motion model

PURPOSE

We introduce and validate a scalable retrospective motion correction technique for brain imaging that incorporates a machine learning component into a model-based motion minimization.

METHODS

A convolutional neural network (CNN) trained to remove motion artifacts from 2D T2 -weighted rapid acquisition with refocused echoes (RARE) images is introduced into a model-based data-consistency optimization to jointly search for 2D motion parameters and the uncorrupted image. Our separable motion model allows for efficient intrashot (line-by-line) motion correction of highly corrupted shots, as opposed to previous methods which do not scale well with this refinement of the motion model. Final image generation incorporates the motion parameters within a model-based image reconstruction. The method is tested in simulations and in vivo motion experiments of in-plane motion corruption.

RESULTS

While the convolutional neural network alone provides some motion mitigation (at the expense of introduced blurring), allowing it to guide the iterative joint-optimization both improves the search convergence and renders the joint-optimization separable. This enables rapid mitigation within shots in addition to between shots. For 2D in-plane motion correction experiments, the result is a significant reduction of both image space root mean square error in simulations, and a reduction of motion artifacts in the in vivo motion tests.

CONCLUSION

The separability and convergence improvements afforded by the combined convolutional neural network+model-based method shows the potential for meaningful postacquisition motion mitigation in clinical MRI.