We introduce a generative smoothness regularization on manifolds (SToRM) model for the recovery of dynamic image data from highly undersampled measurements. The model assumes that the images in the dataset are non-linear mappings of low-dimensional latent vectors. We use the deep convolutional neural network (CNN) to represent the non-linear transformation. The parameters of the generator as well as the low-dimensional latent vectors are jointly estimated only from the undersampled measurements. This approach is different from traditional CNN approaches that require extensive fully sampled training data. We penalize the norm of the gradients of the non-linear mapping to constrain the manifold to be smooth, while temporal gradients of the latent vectors are penalized to obtain a smoothly varying time-series. The proposed scheme brings in the spatial regularization provided by the convolutional network. The main benefit of the proposed scheme is the improvement in image quality and the orders-of-magnitude reduction in memory demand compared to traditional manifold models. To minimize the computational complexity of the algorithm, we introduce an efficient progressive training-in-time approach and an approximate cost function. These approaches speed up the image reconstructions and offers better reconstruction performance.

Bilinear models such as low-rank and dictionary methods, which decompose dynamic data to spatial and temporal factor matrices are powerful and memory-efficient tools for the recovery of dynamic MRI data. Current bilinear methods rely on sparsity and energy compaction priors on the factor matrices to regularize the recovery. Motivated by deep image prior, we introduce a novel bilinear model, whose factor matrices are generated using convolutional neural networks (CNNs). The CNN parameters, and equivalently the factors, are learned from the undersampled data of the specific subject. Unlike current unrolled deep learning methods that require the storage of all the time frames in the dataset, the proposed approach only requires the storage of the factors or compressed representation; this approach allows the direct use of this scheme to large-scale dynamic applications, including free breathing cardiac MRI considered in this work. To reduce the run time and to improve performance, we initialize the CNN parameters using existing factor methods. We use sparsity regularization of the network parameters to minimize the overfitting of the network to measurement noise. Our experiments on free-breathing and ungated cardiac cine data acquired using a navigated golden-angle gradient-echo radial sequence show the ability of our method to provide reduced spatial blurring as compared to classical bilinear methods as well as a recent unsupervised deep-learning approach.

Objective . We introduce an unsupervised motion-compensated reconstruction scheme for high-resolution free-breathing pulmonary magnetic resonance imaging. Approach . We model the image frames in the time series as the deformed version of the 3D template image volume. We assume the deformation maps to be points on a smooth manifold in high-dimensional space. Specifically, we model the deformation map at each time instant as the output of a CNN-based generator that has the same weight for all time-frames, driven by a low-dimensional latent vector. The time series of latent vectors account for the dynamics in the dataset, including respiratory motion and bulk motion. The template image volume, the parameters of the generator, and the latent vectors are learned directly from the k-t space data in an unsupervised fashion. Main results . Our experimental results show improved reconstructions compared to state-of-the-art methods, especially in the context of bulk motion during the scans. Significance . The proposed unsupervised motion-compensated scheme jointly estimates the latent vectors that capture the motion dynamics, the corresponding deformation maps, and the reconstructed motion-compensated images from the raw k-t space data of each subject. Unlike current motion-resolved strategies, the proposed scheme is more robust to bulk motion events during the scan.

In the paper, the authors establish two identities to express higher order derivatives and integer powers of the generating function of the Chebyshev polynomials of the second kind in terms of integer powers and higher order derivatives of the generating function of the Chebyshev polynomials of the second kind respectively, find an explicit formula and an identity for the Chebyshev polynomials of the second kind, conclude the inverse of an integer, unit, and lower triangular matrix, derive an inversion theorem, present several identities of the Catalan numbers, and give some remarks on the closely related results including connections of the Catalan numbers with the Chebyshev polynomials of the second kind, the central Delannoy numbers, and the Fibonacci polynomials respectively.

Introduction: A network meta-analysis was conducted to regard the effects of available immunosuppressive medications in pediatric frequently-relapsing nephrotic syndrome (FRNS) and steroid-dependent nephrotic syndrome (SDNS). Methods: We reviewed systematically 26 randomized controlled trials (1311 patients) that compared any of the following immunosuppressive agents to placebo/nontreatment (P/NT) or another drug for FRNS/SDNS treatment in children. Results: The main outcomes were efficacy and acceptability. At the 6-month, cyclophosphamide, chlorambucil, levamisole, and rituximab had better efficacy than P/NT (odds ratio [OR]: 0.09, 0.03, 0.28, and 0.07, respectively); cyclophosphamide was significantly more effective than azathioprine and chlorambucil. At 12 months, cyclophosphamide, chlorambucil, cyclosporine, levamisole, and rituximab had better efficacy than P/NT (0.10, 0.03, 0.10, 0.23, and 0.07, respectively); Chlorambucil were found to be more efficacious than levamisole and MMF (0.12 and 0.09, respectively). At 24 months, cyclophosphamide, chlorambucil, and levamisole had better efficacy than P/NT (0.09, 0.04, and 0.03, respectively); cyclophosphamide had better efficacy than cyclosporine and vincristine (0.17 and 0.39, respectively). Conclusion: No significant differences in acceptability were found. Our results suggest that cyclophosphamide may be preferred initially in children with FRSN/SDNS, chlorambucil, and rituximab may be acceptable medications for patients with FRSN/SDNS. Long-term follow-up trials focused on gonadal toxicity and limitation of maximum dosage of cyclophosphamide should been carried out.

Current deep learning-based manifold learning algorithms such as the variational autoencoder (VAE) require fully sampled data to learn the probability density of real-world datasets. However, fully sampled data is often unavailable in a variety of problems, including the recovery of dynamic and high-resolution magnetic resonance imaging (MRI). We introduce a novel variational approach to learn a manifold from undersampled data. The VAE uses a decoder fed by latent vectors, drawn from a conditional density estimated from the fully sampled images using an encoder. Since fully sampled images are not available in our setting, we approximate the conditional density of the latent vectors by a parametric model whose parameters are estimated from the undersampled measurements using back-propagation. We use the framework for the joint alignment and recovery of multi-slice free breathing and ungated cardiac MRI data from highly undersampled measurements. Experimental results demonstrate the utility of the proposed scheme in dynamic imaging alignment and reconstructions.