Recent research in off-the-grid compressed sensing (CS) has demonstrated that, under certain conditions, one can successfully recover a spectrally sparse signal from a few time-domain samples even though the dictionary is continuous. In particular, atomic norm minimization was proposed in \cite{tang2012csotg} to recove…
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48 results for “atomic-norm minimization”
The paper improves tensor completion bounds using spectral gap.
problem Theoretical limitations in tensor completion, especially for deterministic sampling.
method Bounding the generalization error of tensor completion methods using spectral gap.
result Improved bounds on tensor completion error, reducing rank dependence.
This work proves exact low tubal rank tensor recovery from Gaussian measurements.
problem Low rank tensor recovery from Gaussian measurements.
method Careful choice of atomic set and computation of Gaussian width for atomic norm.
result Exact recovery of tensors with tubal rank from Gaussian measurements.
In many signal processing applications, the aim is to reconstruct a signal that has a simple representation with respect to a certain basis or frame. Fundamental elements of the basis known as "atoms" allow us to define "atomic norms" that can be used to formulate convex regularizations for the reconstruction problem. …
New method reduces tensor completion sample complexity to nearly optimal levels.
problem Low rank tensor completion with noisy measurements.
method Using atomic-norm and max-quasi-norm for tensor completion.
result Optimal sample complexity of achieved for tensor completion.
Convexifying Sparse Interpolation with Infinitely Wide Neural Networks: An Atomic Norm Approachcs.LG
This study uses neural networks to solve interpolation problems with sparse, infinitely wide layers.
problem Exact data interpolation using sparse, infinitely wide neural networks.
method Atomic norm framework to derive convex hulls and equivalent convex formulations.
result Simple characterizations of convex hulls for different constraints on network weights and biases.
This paper is concerned about sparse, continuous frequency estimation in line spectral estimation, and focused on developing gridless sparse methods which overcome grid mismatches and correspond to limiting scenarios of existing grid-based approaches, e.g., optimization and SPICE, with an infinitely dense grid…
New method recovers radar and communication signals from overlaid data.
problem Recover radar and communication signals from overlaid data with unknown parameters.
method Propose minimizing the sum of multivariate atomic norms (SoMAN) for multi-antenna receiver.
result Minimum number of samples and antennas required for perfect recovery is logarithmically dependent on the maximum of radar targets and communications paths.
Paper proposes a blind predictor for unknown PSD Gaussian process.
problem Predicting a circular symmetric zero-mean stationary Gaussian process with unknown PSD.
method Random spectral representation and atomic-norm minimization for blind estimation.
result The proposed blind predictor performs comparably to an MMSE predictor with known PSD.
Proposes an algorithm for infinite-dimensional sparse learning in system identification.
problem System identification without known model structures.
method Atomic norm regularization and greedy algorithm for solving an infinite-dimensional group lasso problem.
result The proposed algorithm outperforms benchmark methods in impulse response fitting and pole location estimation.
New nonconvex methods improve SysID efficiency and accuracy.
problem Efficiently identify low-order linear systems from limited data.
method Proposes two nonconvex reformulations of Hankel-rank minimization for SysID.
result Nonconvex methods achieve lower statistical error rates and sample complexities.
New method selects variables in groups with few nonzeros, improving support recovery.
problem Structured variable selection with sparse patterns across groups.
method Composite norm and proximal algorithm for exclusive group sparsity.
result Asymptotic consistency in signed support recovery under conventional assumptions.
Beurling-Selberg Extremization for Dual-Blind Deconvolution Recovery in Joint Radar-Communicationscs.IT
Optimal joint separation condition for radar and communications channels in dual-blind deconvolution.
problem Recovering information from overlaid radar and communications signals with unknown channels.
method Extremal functions from Beurling-Selberg interpolation theory for joint separation, nuclear norm minimization for matrix retrieval, and MUSIC for parameter estimation.
result Guaranteed well-conditioned Vandermonde matrix for MUSIC, validating theoretical findings.
Based on a new atomic norm, we propose a new convex formulation for sparse matrix factorization problems in which the number of nonzero elements of the factors is assumed fixed and known. The formulation counts sparse PCA with multiple factors, subspace clustering and low-rank sparse bilinear regression as potential ap…
New method tackles nonlinear, infinite-dimensional signal processing problems.
problem Nonlinear, infinite-dimensional signal processing challenges.
method Directly addresses continuous, nonlinear problems as sparse functional optimization.
result Proves no duality gap for non-atomic problems, allowing efficient solution.
Proves no minimal hypersurfaces in regions bounded by minimal cones.
problem Existence of minimal hypersurfaces in bounded regions.
method Analyzes minimal hypersurfaces in Euclidean space.
result No minimal hypersurfaces in regions bounded by unstable minimal cones.
Study shows area-minimizing submanifolds are mostly smooth except for specific types.
problem Understanding when area-minimizing submanifolds are smooth in mod 2 homology.
method Proved area-minimizing submanifolds are not generically smooth except for geodesics, minimal surfaces, and minimal hypersurfaces.
result Area-minimizing submanifolds are not generically smooth, except for geodesics, minimal surfaces, and minimal hypersurfaces.
Study shows area-minimizing submanifolds are mostly smooth except for geodesics, minimal surfaces, and hypersurfaces.
problem Understanding when area-minimizing submanifolds are smooth in mod 2 homology.
method Proving the mod 2 area-minimizing submanifolds are smooth in specific cases and establishing lower bounds on singular sets.
result Area-minimizing submanifolds are not generically smooth, except for geodesics, minimal surfaces, and minimal hypersurfaces.
Minimal elastic networksmath.AP
Minimal elastic networks minimize energy and length at fixed angles.
problem Finding optimal network configurations under elastic constraints.
method Minimizing a combination of elastic energy and length.
result Existence and regularity of minimizers with prescribed angles.
Lectures on Minimal Surfacesmath.DG
Explains minimal surfaces and their properties.
problem Understanding minimal surfaces and their characteristics.
method Analyzes various minimal surfaces and their properties.
result Discusses the properties and stability of minimal surfaces.
Minimal Lagrangian submanifolds deform to J-minimal ones under small perturbations.
problem Understanding how minimal Lagrangian submanifolds behave under small perturbations in Kaehler-Einstein manifolds.
method Analyzing the deformation of minimal Lagrangian submanifolds under Kaehler-Einstein perturbations.
result Deformed submanifolds remain J-minimal under certain conditions.
Minimal networks minimize length and mass in certain configurations.
problem Finding minimal networks that minimize length and mass.
method Global and local calibrations to prove minimization properties.
result Minimal networks minimize mass and interfaces in partitions.
The study finds conditions for area-minimizing cones over submanifolds.
problem Conditions for area-minimizing cones over submanifolds.
method General configuration results for area-minimizing cones.
result Cone over the minimal product of submanifolds and spheres are area-minimizing.
The paper studies deformations of singular minimal hypersurfaces in dimensions 7 and above.
problem The behavior of singular minimal hypersurfaces in dimensions 7 and above.
method Analyzes the local behavior of minimal hypersurfaces under perturbations and convergence of families of hypersurfaces.
result Existence and smoothness of nearby minimal hypersurfaces under perturbations, uniqueness of homological minimization, and existence of Jacobi fields.
New cones found in sphere foliations, minimizing in most dimensions.
problem Finding new minimizing cones in sphere foliations.
method Analyzing isoparametric foliations and their associated minimal surfaces.
result Most cones over focal submanifolds and products of minimal isoparametric hypersurfaces are minimizing.
Minimal surfaces in 3-sphere created by reflections from polygons, with new examples based on pentagons.
problem Constructing minimal surfaces in 3-sphere using reflections.
method Minimal -gon solves free boundary problem; curvature lines combinatorics investigated.
result New examples of minimal reflection surfaces based on pentagons.
Minimal graphs in Heisenberg group are stable and area-minimizing.
problem Existence and uniqueness of minimal graphs in Heisenberg group.
method Proof of stability and area-minimizing property of minimal graphs.
result Existence and uniqueness of smooth minimal graphs with small boundary.
Study on minimal surfaces in a 3D space with 2m-norm.
problem Characterizing minimal surfaces in a specific geometric space.
method Examining translation, homothetical, and separable minimal surfaces.
result New insights into minimal surfaces in a 3D space with 2m-norm.
Study counts minimal surfaces in curved 3D spaces, finding hyperbolic space minimizes area.
problem Counting minimal surfaces in negatively curved 3-manifolds.
method Introduced an asymptotic quantity to count area-minimizing surfaces and showed minimization by hyperbolic metric.
result Hyperbolic metric minimizes the quantity of area-minimizing surfaces in negatively curved 3-manifolds.
Proves unique continuation for area minimizing currents.
problem Ensuring area minimizing currents match minimal surfaces.
method Analyzes infinite order contact between currents and minimal surfaces.
result Currents and minimal surfaces coincide in a neighborhood.
New inequality helps map stability in minimal surfaces.
problem Stability of minimal surfaces in .
method Developing new inequalities and perspectives on minimal surfaces.
result Reproves instability of classical minimal surfaces like Enneper.
Study removes singularities from area-minimizing surfaces.
problem Removal of singularities from area-minimizing surfaces.
method Extending results on area-minimizing cones to handle isolated singularities.
result Isolated singularities can be locally perturbed away on the minimizing side.
Minimal submanifolds in spheres can be produced via Clifford type minimal products, and their Morse indices and nullities are calculated.
problem Understanding the properties of minimal submanifolds in spheres via Clifford products.
method Analyzing the first eigenfunctions and Morse indices of minimal products of minimal submanifolds.
result The Morse index and nullity of the minimal product are calculated and shown for specific cases.
Minimal generating sets of Reidemeister moves identified and classified.
problem Classifying minimal generating sets of Reidemeister moves.
method Determined minimal generating sets, provided classifications, and identified candidates.
result 12 out of 16 candidates for minimal generating sets were proven minimal.
Round balls minimize liquid drop model volumes ≤ 1.
problem Minimizing volumes in liquid drop models.
method Proved uniqueness of minimizers for small volumes.
result Round balls uniquely minimize volumes ≤ 1.
In this paper, we prove that every conformal minimal immersion of a compact bordered Riemann surface into a minimally convex domain can be approximated, uniformly on compacts in , by proper complete conformal minimal immersions . We also obtain a …
The paper creates symmetrical discrete minimal nets using Schwarz reflection.
problem Creating symmetrical discrete minimal nets.
method Extending Schwarz reflection principle to discrete minimal surfaces.
result Global examples of discrete minimal nets with high symmetry.
Recent progress on minimal surface system and cones in Euclidean spaces.
problem Exploring the Dirichlet problem for minimal surfaces and cones.
method Systematic developments and new families of minimizing cones.
result New families of minimizing cones of different types.
Newly confirmed area-minimizing properties of Lawson-Osserman cones.
problem Verifying the area-minimizing property of Lawson-Osserman cones.
method Analyzing cones of type (n, p, 2) constructed in [XYZ].
result All Lawson-Osserman cones of type (n, p, 2) are area-minimizing.
New minimal surfaces grow area very quickly.
problem Understanding minimal surfaces with rapid area growth.
method Examples of minimal immersions in Euclidean space.
result Proper minimal surfaces with rapid area growth found.
New minimal surfaces found with Cantor ends in convex domains.
problem Finding complex structures for minimal surfaces with Cantor ends.
method Proving existence of complete minimal surfaces with Cantor ends in minimally convex domains.
result Existence of a Cantor set whose complement forms a complete minimal surface.
Study on minimal hypersurfaces in a special normed space.
problem Characterizing minimal hypersurfaces in a specific normed space.
method Investigate translation and separable minimal hypersurfaces.
result New insights into the properties of minimal hypersurfaces.
The study proves that certain stable minimal hypersurfaces must be cylindrical.
problem Characterizing stable minimal hypersurfaces in Euclidean space.
method Analyzing the density at infinity and using stable area minimizing hypercone properties.
result Stable minimal hypersurfaces with specific conditions are cylindrical.
Every point on an asymptotically flat 3D space has a minimal plane nearby.
problem Finding minimal surfaces in asymptotically flat 3D spaces.
method Proving the existence of minimal planes for every point in the manifold.
result Every point in an asymptotically flat 3D space has a complete properly embedded minimal plane.
Minimal surfaces help compare geometric shapes.
problem Comparing different geometric shapes.
method Applications of minimal surfaces.
result New insights into geometric comparisons.
Minimal partitions with minimal perimeter found in metric spaces.
problem Finding minimal partitions with minimal perimeter in metric spaces.
method Existence proof and regularity analysis of minimal domains.
result Existence and regularity of minimal partitions in various metric spaces.
The paper studies minimal submanifolds with specific curvature properties in Euclidean space.
problem Minimal submanifolds with -umbilical properties in Euclidean space.
method Established a correspondence and developed a Weierstrass type method for local parametrization.
result Minimal, generic, -umbilic submanifolds are -rotational and have a parametric description.
Proves minimal crossing diagrams for specific spatial graphs.
problem Proving minimal crossing diagrams for spatial graphs.
method Analyzing adequate diagrams and replacing vertices and edges.
result All 1-vertex spatial graphs with adequate diagrams have minimal crossing number.