arXiv research

Enhances MRI image quality with Conditional WGAN and adaptive balancing.

The annihilating filter-based low-rank Hankel matrix approach (ALOHA) is one of the state-of-the-art compressed sensing approaches that directly interpolates the missing k-space data using low-rank Hankel matrix completion. The success of ALOHA is due to the concise signal representation in the k-space domain thanks to…

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 …

A new deep learning model speeds up MRI by reconstructing from undersampled data.

This paper presents a deep learning method for faster magnetic resonance imaging (MRI) by reducing k-space data with sub-Nyquist sampling strategies and provides a rationale for why the proposed approach works well. Uniform subsampling is used in the time-consuming phase-encoding direction to capture high-resolution im…

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…

New unsupervised deep learning method improves temporal resolution in tMRA.

Unpaired deep learning reconstructs MRI images from accelerated data.

Study benchmarks methods for learning non-Cartesian k-space trajectories and reconstruction.

Quantifies Schur's theorem for curves in CAT(k) spaces.

Deep learning improves MRI image quality from down-sampled data.

New method corrects motion artifacts in MR images without paired data.

New method optimizes MRI sampling patterns for faster scans.

Study geodesic mappings and concircular fields in pseudo-Riemannian manifolds.

Deep learning speeds up MRI image reconstruction from sparse data.

Paper studies weighted Fermat-Frechet problem for simplex edge lengths.

Decreasing magnetic resonance (MR) image acquisition times can potentially reduce procedural cost and make MR examinations more accessible. Compressed sensing (CS)-based image reconstruction methods, for example, decrease MR acquisition time by reconstructing high-quality images from data that were originally sampled a…

New method glues Lorentzian spaces, preserving curvature bounds.

Dual U-net models improve multi-channel MRI image reconstruction.

The paper proves inequalities linking Wasserstein distances and eigenfunctions in RCD(K,∞) spaces.

It is well known that the space of oriented lines of Euclidean space has a natural symplectic structure. Moreover, given an immersed, oriented hypersurface S the set of oriented lines that cross S orthogonally is a Lagrangian submanifold. Conversely, if \bar{S} an n-dimensional family of oriented lines is Lagrangian, t…

DeepcomplexMRI uses deep residual networks for faster MRI imaging.

Defines curvature for metric triples in metric spaces.

AFP-CKSAAP predicts antifreeze proteins using k-spaced amino acid pairs with deep neural networks.

The paper shows neural networks can approximate functions over non-compact domains with non-polynomial activation.

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…

In this paper, we show a local energy convexity of $W^{1,2}$ maps into $CAT(K)$ spaces. This energy convexity allows us to extend Colding and Minicozzi's width-sweepout construction to produce closed geodesics in any closed Alexandrov space of curvature bounded from above, which also provides a generalized version of t…

This article is a survey article on geometric group theory from the point of view of a non-expert who likes geometric group theory and uses it in his own research. The sections are: classical examples, basics about quasiisometry,properties and invariants of groups invariant under quasiisometry, rigidity, hyperbolic spa…

Let $M_k$ be the complete, simply connected, Riemannian 2-manifold of constant curvature $k \le 0$. Let $E$ be a closed, simply connected subspace of $M_k$ with the property that every two points in $E$ is connected by a rectifiable path in $E$. We show that under the induced path metric, $E$ is a complete CAT($k$) spa…

Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing exploits the sparsity of images or image patches in a transform domain or synth…

Ensembled neural networks improve MRI image quality.

Paper develops a novel kernel-based method for MRI data recovery.

Harmonic maps from surfaces to CAT(k) spheres are branched coverings.

New neural network improves MRI reconstruction for non-Cartesian data.

New method recovers classical cut and paste groups for manifolds.

Study proposes a new method for MRI image reconstruction using denoising autoencoders and undecimated wavelet transforms.

We introduce an analogue of the theory of length spaces into the setting of Lorentzian geometry and causality theory. The rôle of the metric is taken over by the time separation function, in terms of which all basic notions are formulated. In this way we recover many fundamental results in greater generality, while at …

It is well known that in compact local Lipschitz neighborhood retracts in Euclidean space flat convergence for integer rectifiable currents amounts just to weak convergence. In the present paper we extend this result to integral currents in complete metric spaces admitting a local cone type inequality. These include in…

Acquisition of Magnetic Resonance Imaging (MRI) scans can be accelerated by under-sampling in k-space (i.e., the Fourier domain). In this paper, we consider the problem of optimizing the sub-sampling pattern in a data-driven fashion. Since the reconstruction model's performance depends on the sub-sampling pattern, we c…

Convex hypersurfaces in curved spaces bound convex regions.

Jointly correct bias fields and reconstruct undersampled MRI images.

We show that if G is a discrete subgroup of the group of the isometries of the hyperbolic k-space H^k, and if R is a representation of G into the group of the isometries of H^n, then any R-equivariant map F from H^k to H^n extends to the boundary in a weak sense in the setting of Borel measures. As a consequence of thi…

The paper shows how heat flow approximates area functional on specific geometric spaces.

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 …

Critical nets in k-space have bounded edge lengths and vertices.

F. Labourie [arXiv:1212.5015] characterized the Hitchin components for $\operatorname{PSL}(n, \mathbb{R})$ for any $n>1$ by using the swapping algebra, where the swapping algebra should be understood as a ring equipped with a Poisson bracket. We introduce the rank $n$ swapping algebra, which is the quotient of the swap…

Sparse VAE learns latent factors from high-dimensional data.

Sparse coding approximates the data sample as a sparse linear combination of some basic codewords and uses the sparse codes as new presentations. In this paper, we investigate learning discriminative sparse codes by sparse coding in a semi-supervised manner, where only a few training samples are labeled. By using the m…