Sparse spikes super-resolution on thin grids II: the continuous basis pursuit

DOI10.1088/1361-6420/aa7fcezbMath1392.35332OpenAlexW2608482034MaRDI QIDQ5368862

Gabriel Peyré, Vincent Duval

Publication date: 11 October 2017

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1361-6420/aa7fce

zbMATH Keywords

convex optimizationsparsityLassosuper-resolutioncontinuous basis pursuit (C-BP)first order approximation of the kernelspikes recognition

Mathematics Subject Classification ID

Convex programming (90C25) Optimality conditions and duality in mathematical programming (90C46) Approximation methods and heuristics in mathematical programming (90C59) Inverse problems for PDEs (35R30) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Inverse problems in optimal control (49N45)

Related Items (12)

On the uniqueness of solutions for the basis pursuit in the continuum ⋮ ``FISTA in Banach spaces with adaptive discretisations ⋮ Thresholding gradient methods in Hilbert spaces: support identification and linear convergence ⋮ TV-based reconstruction of periodic functions ⋮ On formulae for the Moore-Penrose inverse of a columnwise partitioned matrix ⋮ Multi-kernel unmixing and super-resolution using the modified matrix pencil method ⋮ The sliding Frank–Wolfe algorithm and its application to super-resolution microscopy ⋮ Modern regularization methods for inverse problems ⋮ Sparse Inverse Problems over Measures: Equivalence of the Conditional Gradient and Exchange Methods ⋮ Sparsest piecewise-linear regression of one-dimensional data ⋮ The basins of attraction of the global minimizers of the non-convex sparse spike estimation problem ⋮ TV-based spline reconstruction with Fourier measurements: uniqueness and convergence of grid-based methods

Uses Software

• PDCO

Cites Work

• Unnamed Item
• Exact reconstruction using Beurling minimal extrapolation
• Super-resolution from noisy data
• Support recovery for sparse super-resolution of positive measures
• Particular formulae for the Moore--Penrose inverse of a columnwise partitioned matrix
• Exact support recovery for sparse spikes deconvolution
• An introduction to \(\Gamma\)-convergence
• Spike detection from inaccurate samplings
• On Sparse Representations in Arbitrary Redundant Bases
• Atomic Decomposition by Basis Pursuit
• Variational Analysis
• Recovery of Sparse Translation-Invariant Signals With Continuous Basis Pursuit
• Inverse problems in spaces of measures
• Superresolution without separation
• Sparse regularization on thin grids I: the Lasso
• Towards a Mathematical Theory of Super‐resolution
• Convex analysis and monotone operator theory in Hilbert spaces

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