Support detection in super-resolution
arXiv:1302.3921
Abstract
We study the problem of super-resolving a superposition of point sources from noisy low-pass data with a cut-off frequency f. Solving a tractable convex program is shown to locate the elements of the support with high precision as long as they are separated by 2/f and the noise level is small with respect to the amplitude of the signal.
References in corpus (1)
Cited by in corpus (33)
- Direction of Arrival Estimation Using Co-prime Arrays: A Super Resolution Viewpoint
- Harnessing Sparsity over the Continuum: Atomic Norm Minimization for Super Resolution
- Guaranteed Blind Sparse Spikes Deconvolution via Lifting and Convex Optimization
- The recoverability limit for superresolution via sparsity
- Super-resolution on the Sphere using Convex Optimization
- Stable super-resolution limit and smallest singular value of restricted Fourier matrices
- Stable Support Recovery of Stream of Pulses with Application to Ultrasound Imaging
- MUSIC for Single-Snapshot Spectral Estimation: Stability and Super-resolution
- Near Minimax Line Spectral Estimation
- Exact Support Recovery for Sparse Spikes Deconvolution
- Super-resolution, Extremal Functions and the Condition Number of Vandermonde Matrices
- Greed is Super: A Fast Algorithm for Super-Resolution
- Sparse Spikes Deconvolution on Thin Grids
- Exact solutions to Super Resolution on semi-algebraic domains in higher dimensions
- Sparse Recovery Beyond Compressed Sensing: Separable Nonlinear Inverse Problems
- Support Recovery for Sparse Deconvolution of Positive Measures
- Elementary error estimates for super-resolution de-noising
- Algorithmic Foundations for the Diffraction Limit
- Spike detection from inaccurate samplings
- Accuracy of spike-train Fourier reconstruction for colliding nodes
- Support Localization and the Fisher Metric for off-the-grid Sparse Regularization
- A Theory of Computational Resolution Limit for Line Spectral Estimation
- Towards optimal sensor placement for inverse problems in spaces of measures
- A mathematical theory of computational resolution limit in one dimension
- On the Stable Resolution Limit of Total Variation Regularization for Spike Deconvolution
- Stable Super-Resolution of Images: A Theoretical Study
- A Super-Resolution Framework for Tensor Decomposition
- Non-uniform spline recovery from small degree polynomial approximation
- FastPart: Over-Parameterized Stochastic Gradient Descent for Sparse optimisation on Measures
- Data-driven Estimation of Sinusoid Frequencies
- Sparse Inverse Problems Over Measures: Equivalence of the Conditional Gradient and Exchange Methods
- Super-resolution estimation of cyclic arrival rates
- Unified Convex Optimization Approach to Super-Resolution Based on Localized Kernels