Reconstructing a planar domain from its Dirichlet-to-Neumann data
problem Reconstructing a planar domain from its Dirichlet-to-Neumann data
method Using the Hilbert transform of the boundary curve
result Reconstructing a simply connected planar domain from the DN data
Develops GNNs for incomplete graphs, improving learning from missing node attributes.
problem Learning from incomplete graphs with missing node attributes.
method Introduces PaGNNs with novel partial aggregation functions for incomplete graph data.
result Demonstrates effectiveness and efficiency of PaGNNs on various datasets.
We consider the problem of developing a method to reconstruct a potential q from the partial data Dirichlet-to-Neumann map for the Schrödinger equation (−Δg+q)u=0 on a fixed admissible manifold (M,g). If the part of the boundary that is inaccessible for measurements satisfies a flatness condition in one directio…
The article recovers tensor fields from partial data using weighted divergent ray transforms.
problem Recovering tensor fields from partial data.
method Weighted divergent ray transforms, unique continuation property of fractional Laplacian, explicit reconstruction formulas.
result Recovery of symmetric m-tensor fields and unique continuation for vector fields and symmetric 2-tensor fields. Single linear solve combines surface reconstruction and uncertainty quantification.
problem Reconstructing surfaces from partial point clouds with uncertainty.
method Geometric Gaussian processes for stochastic surface reconstruction.
result Single linear solve for surface reconstruction with probabilistic capabilities.
Deep learning scheme identifies and reconstructs chaotic and stochastic systems from noisy data.
problem Challenging identification of governing equations from noisy and partial observations.
method Jointly learns inference model and governing laws using variational deep learning.
result Framework generalizes state-of-the-art methods and accounts for stochastic variabilities.
Algebras of smooth functions help reconstruct bulk topological types.
problem Reconstructing the smooth topological type of a compact manifold from its boundary.
method Introducing subalgebras of boundary functions and proving their tensor product reconstruction of the bulk algebra.
result The topological algebras A(v) and B(f) allow for the recovery of the smooth topological type of the bulk X. Reconstruct flows and manifolds from their boundary actions on circles.
problem Understanding and reconstructing flows and manifolds from their boundary actions.
method Reconstructing flows and manifolds from actions on circles with invariant almost laminations.
result Reconstructs flows and manifolds from their boundary actions, including pseudo-Anosov flows in 3-manifolds.
The paper recovers contact forms from boundary data using vector fields and Lyapunov functions.
problem Recovering contact forms from boundary data.
method Using vector fields and Lyapunov functions, the paper describes boundary data and proves reconstruction of (X,β) up to diffeomorphism. result Boundary data allow for the reconstruction of (X,β) up to a diffeomorphism of X. New method reconstructs data subsets from limited published statistics.
problem Reconstructing tabular data from aggregate statistics when full datasets are not possible.
method Generates and verifies subsets of rows and columns that are guaranteed to be correct.
result Privacy violations can persist even with sparse published statistics.
Survey on inverse exponential Radon transform methods.
problem Analytical methods for inverse exponential Radon transform.
method Derivation of classical inversion formula, finite Hilbert transform, exact reconstruction from partial measurements, diverging-beam data.
result Exact reconstruction from 180 degree data using finite Hilbert transform.
We consider the problem of approximately reconstructing a partially-observed, approximately low-rank matrix. This problem has received much attention lately, mostly using the trace-norm as a surrogate to the rank. Here we study low-rank matrix reconstruction using both the trace-norm, as well as the less-studied max-no…
Spreading processes are often modelled as a stochastic dynamics occurring on top of a given network with edge weights corresponding to the transmission probabilities. Knowledge of veracious transmission probabilities is essential for prediction, optimization, and control of diffusion dynamics. Unfortunately, in most ca…
Paper reconstructs compact Riemannian manifolds from travel time data.
problem Reconstructing compact Riemannian manifolds from partial travel time data.
method Embedding in function space, studying distance function regularity.
result Reconstruction of compact Riemannian manifolds from travel time data.
Measures time-delay embedding for noisy, sparse data.
problem Applying Takens' embedding theorem to real-world, noisy data.
method Formulated a measure-theoretic generalization of the embedding theorem, using optimal transport.
result Reconstructed full state of dynamical systems from time-lagged partial observations robust to noise and sparsity.
Compressed sensing is a powerful tool in applications such as magnetic resonance imaging (MRI). It enables accurate recovery of images from highly undersampled measurements by exploiting the sparsity of the images or image patches in a transform domain or dictionary. In this work, we focus on blind compressed sensing (…
Auto-encoder model simplifies industrial sensor data into fixed-length vectors.
problem Efficiently summarizing large-scale industrial sensor signals.
method Recurrent auto-encoder with partial reconstruction and rolling window approach.
result Fixed-length vectors capture selected features over time.
For a given smooth compact manifold M, we introduce an open class G(M) of Riemannian metrics, which we call \emph{metrics of the gradient type}. For such metrics g, the geodesic flow vg on the spherical tangent bundle SM→M admits a Lyapunov function (so the vg-flow is traversing). It turns ou…
We investigate the reduction process of a k-symplectic field theory whose Lagrangian is invariant under a symmetry group. We give explicit coordinate expressions of the resulting reduced partial differential equations, the so-called Lagrange-Poincare field equations. We discuss two issues about reconstructing a solutio…
Reconstructing manifolds from partial distance and heat kernel data.
problem Reconstructing a manifold from noisy distance measurements and heat kernel data.
method Approximate reconstruction of a manifold from partial distance and heat kernel data with noise.
result A stable reconstruction of the manifold can be achieved from noisy heat kernel data.
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…
ROAD-EnKFs use learned low-dimensional models to improve state reconstruction and forecasting.
problem Reconstructing and forecasting states of unknown or expensive systems.
method Learned low-dimensional surrogate models and ensemble Kalman filter integration.
result ROAD-EnKFs achieve higher accuracy at lower computational cost than existing methods.
We give a completely formalized definition of a notion of " general manifold ". It turns out that " gluing data " form an equivalence-partially ordered set (e-pos), which is a special instance of an ordered groupoid. We state and prove reconstruction theorems, allowing to reconstruct general manifolds and their mor-phi…
Improved latent dynamics identification framework reduces training time and improves accuracy.
problem Accurate numerical solutions of partial differential equations require computationally expensive solvers.
method Sequential decoder training (mLaSDI) to correct residual errors from previous stages.
result mLaSDI consistently outperforms standard LaSDI, achieving lower prediction errors and reduced training time.
Given a bounded domain M in Rn with a conformally Euclidean metric g=ρdx2, in this paper we consider the inverse problem of recovering a semigeodesic neighborhood of a domain Γ⊂∂M and the conformal factor ρ in the neighborhood from the travel time data (defined below) and the Carte…
APGD algorithm reconstructs point set from partial distance measurements.
problem Reconstructing point set configuration from partial Euclidean distance measurements.
method Asymmetric Projected Gradient Descent (APGD) for EDMC problem.
result Global convergence and exact recovery with O(μ2r3κ2nlogn) observations. Instantiation-Net reconstructs 3D mesh from single 2D image for right ventricle.
problem Reconstructing 3D shape from limited 2D images for surgical navigation.
method Combines DCNN for feature extraction and GCN for mesh reconstruction.
result Demonstrates practical strength and potential clinical use.
MKD learns MTS attributes to reconstruct and cluster unseen classes.
problem Reconstructing and clustering unseen multivariate time-series.
method Multiple-kernel dictionary learning (MKD) to learn semantic attributes.
result MKD provides interpretable reconstruction and high clustering performance.
The natural partial ordering of the orbit types of the action of the group of local gauge transformations on the space of connections in space-time dimension d<=4 is investigated. For that purpose, a description of orbit types in terms of cohomology elements of space-time, derived earlier, is used. It is shown that, on…
An important problem of reconstruction of diffusion network and transmission probabilities from the data has attracted a considerable attention in the past several years. A number of recent papers introduced efficient algorithms for the estimation of spreading parameters, based on the maximization of the likelihood of …
Reconstruct cohomology and homology from compact subsets and nerves.
problem Reconstructing cohomology and homology from compact subsets and nerves.
method Using Bousfield-Kan/Araki-Yoshimura type spectral sequences and corrected derived limits.
result Corrected derived limits coincide with usual ones when topology is discrete.
Proposes a method to estimate discrete curvatures for image reconstruction.
problem Image reconstruction challenges due to non-convex, non-smooth, and highly non-linear first-order optimal conditions.
method Estimates discrete curvatures (mean and Gaussian) locally using differential geometry theory. Solves a weighted total variation minimization problem efficiently with ADMM.
result Demonstrates the effectiveness and superiority of the proposed variational models for various image reconstruction tasks.
It is shown that if M is a strongly causal free of naked singularities space-time, then its causal structure is completely characterized by a partial order in the space of skies defined by means of a class non-negative Legendrian isotopies. It is also proved that such partial order is determined by the class of futur…
This paper learns variational models and solvers for inverse problems from incomplete data.
problem Solving inverse problems with partially observed data.
method Joint learning of variational cost and gradient-based solver as neural networks.
result Joint learning leads to improved reconstruction performance.
Bayesian method predicts future network configurations from past snapshots.
problem Reconstructing evolving networks from partial observations.
method Bayesian approach using past network snapshots to inform future predictions.
result Method accurately predicts link probabilities and network structure.
The present article proposes a partial answer to the explicit inversion of the tensor tomography problem in two dimensions, by proving injectivity over certain kinds of tensors and providing reconstruction formulas for them. These tensors are symmetric differentials of any order as well as other types obtained after ta…
Reconstructing 3D manifolds from boundary electromagnetic data.
problem Reconstructing a compact, connected, real-analytic Riemannian 3-manifold from tangential electric and magnetic fields on its boundary.
method Factorizing Maxwell's equations and using an isometric transform to reconstruct the metric.
result The electromagnetic Dirichlet-to-Neumann map uniquely determines all derivatives of electromagnetic parameters on the boundary.
HERA improves PLL by integrating heterogeneous loss and sparse-low-rank regularization.
problem Learning from data with partial labels.
method Combines heterogeneous loss and sparse-low-rank regularization.
result Achieves superior performance on artificial and real-world data.
We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruction and PSF…
Mathematical problems of digital terrain analysis include interpolation of digital elevation models (DEMs), DEM generalization and denoising, and computation of morphometric variables by calculation of partial derivatives of elevation. Traditionally, these procedures are based on numerical treatments of two-variable di…
New technique halves scan time for multi-echo MR images.
problem Slow acquisition of multi-echo magnetic resonance images.
method Structured deep dictionary learning for adaptive reconstruction.
result Scan time reduced by half compared to state-of-the-art.
Researchers reconstruct stiffness tensors from limited data in anisotropic elasticity.
problem Reconstructing stiffness tensors from partial data around one polarization.
method Using algebraic geometry and slowness surfaces, the approach leverages the algebraic geometry of families of slowness surfaces.
result For tensors in a dense open subset, a small amount of data around one polarization uniquely determines the entire slowness surface and stiffness tensor.
This work uses diffusion models for accurate signal recovery from semi-parametric models.
problem Recovering signals from semi-parametric single index models with discontinuous link functions.
method Proposes an efficient reconstruction method using diffusion models that requires one round of sampling and inversion.
result Demonstrates more accurate reconstructions with fewer evaluations compared to competing methods.
GeoFunFlow tackles inverse problems on complex geometries with efficient learning.
problem Challenges in inverse problems governed by PDEs, especially on irregular geometries.
method Combines geometric function autoencoder and latent diffusion model trained via rectified flow.
result Achieves state-of-the-art reconstruction accuracy and efficient inference.
New method speeds up kernel-based machine learning for force field reconstruction.
problem Scalability issues in kernel-based machine learning for force field reconstruction.
method Nyström-type methods to construct preconditioners based on low-rank approximations of the kernel matrix.
result Effective preconditioners lead to super-linear convergence in kernel-based machine learning.
New method reconstructs interbank networks enforcing reciprocity to improve stability and risk prediction.
problem Lack of public interbank network data and difficulty in replicating cycles.
method Proposes a new network reconstruction method enforcing sparsity and link reciprocity from aggregate data.
result Adding reciprocity improves prediction of network properties, including largest real eigenvalue and eccentricity of eigenvalues.
Reconstructing patterns of interconnections from partial information is one of the most important issues in the statistical physics of complex networks. A paramount example is provided by financial networks. In fact, the spreading and amplification of financial distress in capital markets is strongly affected by the in…
SANs use sparse activation functions to compress data representations.
problem Learning meaningful features without considering compression.
method Introduce φ metric, define activation functions, and present SANs.
result SANs achieve small description length and interpretable kernels.