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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15 results for “atomic-norm”
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. …
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…
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.
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.
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.
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.
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.
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.
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.
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.
In this paper, we study the prediction of a circularly symmetric zero-mean stationary Gaussian process from a window of observations consisting of finitely many samples. This is a prevalent problem in a wide range of applications in communication theory and signal processing. Due to stationarity, when the autocorrelati…
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.