arXiv research

The paper studies Möbius energy gradient of helix pairs and finds limiting behavior as coiling ratio increases.

Study on helix curves and their Möbius energy asymptotics.

In order to ensure trouble-free operation, prediction of hardware failures is essential. This applies especially to medical systems. Our goal is to determine hardware which needs to be exchanged before failing. In this work, we focus on predicting failures of 20-channel Head/Neck coils using image-related measurements.…

Fast and accurate MRI image reconstruction from undersampled data is crucial in clinical practice. Deep learning based reconstruction methods have shown promising advances in recent years. However, recovering fine details from undersampled data is still challenging. In this paper, we introduce a novel deep learning bas…

Already before systems malfunction one has to know if hardware components will fail in near future in order to counteract in time. Thus, unplanned downtime is ought to be avoided. In medical imaging, maximizing the system's uptime is crucial for patients' health and healthcare provider's daily business. We aim to predi…

The U-net is a deep-learning network model that has been used to solve a number of inverse problems. In this work, the concatenation of two-element U-nets, termed the W-net, operating in k-space (K) and image (I) domains, were evaluated for multi-channel magnetic resonance (MR) image reconstruction. The two element net…

We explore an ensembled $Σ$-net for fast parallel MR imaging, including parallel coil networks, which perform implicit coil weighting, and sensitivity networks, involving explicit sensitivity maps. The networks in $Σ$-net are trained in a supervised way, including content and GAN losses, and with various ways of data c…

Study on the $L^p$ behavior of helix curves' energy density.

In recent years, several families of hyperbolic knots have been shown to have both volume and $λ_1$ (first eigenvalue of the Laplacian) bounded in terms of the twist number of a diagram, while other families of knots have volume bounded by a generalized twist number. We show that for general knots, neither the twist nu…

Algorithms for Magnetic Resonance (MR) image reconstruction from undersampled measurements exploit prior information to compensate for missing k-space data. Deep learning (DL) provides a powerful framework for extracting such information from existing image datasets, through learning, and then using it for reconstructi…

We present simple reconstruction networks for multi-coil data by extending deep cascade of CNN's and exploiting the data consistency layer. In particular, we propose two variants, where one is inspired by POCSENSE and the other is calibration-less. We show that the proposed approaches are competitive relative to the st…

Time-resolved angiography with interleaved stochastic trajectories (TWIST) has been widely used for dynamic contrast enhanced MRI (DCE-MRI). To achieve highly accelerated acquisitions, TWIST combines the periphery of the k-space data from several adjacent frames to reconstruct one temporal frame. However, this view-sha…

XPDNet wins MRI reconstruction challenge with neural network.

A benchmarking framework for studying data geometry.

We introduce a new unsupervised representation learning and visualization using deep convolutional networks and self organizing maps called Deep Neural Maps (DNM). DNM jointly learns an embedding of the input data and a mapping from the embedding space to a two-dimensional lattice. We compare visualizations of DNM with…

New Bayesian method for joint sparse parameter inference.

The approximation of nonlinear kernels via linear feature maps has recently gained interest due to their applications in reducing the training and testing time of kernel-based learning algorithms. Current random projection methods avoid the curse of dimensionality by embedding the nonlinear feature space into a low dim…

Nyquist ghost artifacts in EPI are originated from phase mismatch between the even and odd echoes. However, conventional correction methods using reference scans often produce erroneous results especially in high-field MRI due to the non-linear and time-varying local magnetic field changes. Recently, it was shown that …

We present a graph-based variational algorithm for classification of high-dimensional data, generalizing the binary diffuse interface model to the case of multiple classes. Motivated by total variation techniques, the method involves minimizing an energy functional made up of three terms. The first two terms promote a …

This study uses CNN-IOs to estimate MRI image reconstruction performance bounds.

It is a well-known procedure for constructing a torus knot or link that first we prepare an unknotted torus and meridian disks in the complementary solid tori of it, and second smooth the intersections of the boundary of meridian disks uniformly. Then we obtain a torus knot or link on the unknotted torus and its Seifer…

We propose a novel end-to-end neural network architecture that, once trained, directly outputs a probabilistic clustering of a batch of input examples in one pass. It estimates a distribution over the number of clusters $k$, and for each $1 \leq k \leq k_\mathrm{max}$, a distribution over the individual cluster assignm…

This paper proposes a multi-channel image reconstruction method, named DeepcomplexMRI, to accelerate parallel MR imaging with residual complex convolutional neural network. Different from most existing works which rely on the utilization of the coil sensitivities or prior information of predefined transforms, Deepcompl…

We present two graph-based algorithms for multiclass segmentation of high-dimensional data. The algorithms use a diffuse interface model based on the Ginzburg-Landau functional, related to total variation compressed sensing and image processing. A multiclass extension is introduced using the Gibbs simplex, with the fun…

We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematical constraints linking the centerline's tangent to the orientation of …

We discuss - in what is intended to be a pedagogical fashion - generalized "mean-to-risk" ratios for portfolio optimization. The Sharpe ratio is only one example of such generalized "mean-to-risk" ratios. Another example is what we term the Fano ratio (which, unlike the Sharpe ratio, is independent of the time horizon)…

Accelerated magnetic resonance (MR) scan acquisition with compressed sensing (CS) and parallel imaging is a powerful method to reduce MR imaging scan time. However, many reconstruction algorithms have high computational costs. To address this, we investigate deep residual learning networks to remove aliasing artifacts …

FORE evaluates occupancy ratios without requiring Bellman completeness.

Optimal option portfolios under Sharpe Ratio maximization with skew-elliptical t-distributed returns

Omega ratio, defined as the probability-weighted ratio of gains over losses at a given level of expected return, has been advocated as a better performance indicator compared to Sharpe and Sortino ratio as it depends on the full return distribution and hence encapsulates all information about risk and return. We comput…

We present a new methodology of computing incremental contribution for performance ratios for portfolio like Sharpe, Treynor, Calmar or Sterling ratios. Using Euler's homogeneous function theorem, we are able to decompose these performance ratios as a linear combination of individual modified performance ratios. This a…

The paper proposes an asset allocation strategy using the Sortino ratio for better performance.

A new ratio, the Hansen ratio, simplifies mean-variance portfolio theory.

Jointly correct bias fields and reconstruct undersampled MRI images.

Develops a new density ratio estimator for causal inference.

New PU ratio predicts long-term Bitcoin returns better than other methods.

The paper studies curves of constant-ratio in pseudo-Galilean space.

Unified framework for OOD detection using class ratio estimation.

Paper shows how to embed Möbius bands with many twists and small aspect ratios.

Direct neural ratio estimator for likelihood-free inference.

Neural networks approximate likelihood ratios for complex models.

Paper tackles unbounded density ratio estimation for covariate shift adaptation.

Calculates twist in Teichmüller space using cross ratios.

Study shows robust method for estimating density ratios even with heavy contamination.

Meta-learning improves relative density-ratio estimation from limited data.

TRE improves density-ratio estimation for highly dissimilar densities.

New method resolves density ratio estimation saturation issues.

The paper describes a method to infer the signal-to-noise ratio in portfolio optimization.