On the uniqueness of solutions for the basis pursuit in the continuum

DOI10.1088/1361-6420/ac9998zbMath1504.94031arXiv2009.11855OpenAlexW4292162877MaRDI QIDQ5044980

Quentin Denoyelle, Julien Fageot, Thomas Debarre

Publication date: 3 November 2022

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

Full work available at URL: https://arxiv.org/abs/2009.11855

zbMATH Keywords

uniquenesstotal variation normbasis pursuitdual certificatesPisarenko decomposition

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Radon transform (44A12) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)

Related Items (2)

Linear inverse problems with nonnegativity constraints: singularity of optimisers ⋮ TV-based spline reconstruction with Fourier measurements: uniqueness and convergence of grid-based methods

Uses Software

• PDCO

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear total variation based noise removal algorithms
• A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
• A mathematical introduction to compressive sensing
• Exact reconstruction using Beurling minimal extrapolation
• Super-resolution from noisy data
• The shaping of the Riesz representation theorem: A chapter in the history of analysis
• Exact support recovery for sparse spikes deconvolution
• A semidefinite programming approach to the generalized problem of moments
• Spline solutions to L\(^1\) extremal problems in one and several variables
• The Lasso problem and uniqueness
• The generalized Lasso problem and uniqueness
• Functional penalised basis pursuit on spheres
• Sparsest piecewise-linear regression of one-dimensional data
• Sparse optimization on measures with over-parameterized gradient descent
• On the linear convergence rates of exchange and continuous methods for total variation minimization
• Spike detection from inaccurate samplings
• Sparse non-negative super-resolution -- simplified and stabilised
• When does OMP achieve exact recovery with continuous dictionaries?
• Atomic Decomposition by Basis Pursuit
• Representer Theorems for Sparsity-Promoting <inline-formula> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math> </inline-formula> Regularization
• Exact Solutions to Super Resolution on Semi-Algebraic Domains in Higher Dimensions
• Sparse and Redundant Representations
• A new approach to variable selection in least squares problems
• Splines Are Universal Solutions of Linear Inverse Problems with Generalized TV Regularization
• Super-resolution of point sources via convex programming
• Towards Generalized FRI Sampling With an Application to Source Resolution in Radioastronomy
• MultiDimensional Sparse Super-Resolution
• Inverse problems in spaces of measures
• Prony methods for recovery of structured functions
• Stable super-resolution of images: theoretical study
• TV-based reconstruction of periodic functions
• A fast homotopy algorithm for gridless sparse recovery
• The sliding Frank–Wolfe algorithm and its application to super-resolution microscopy
• The ML–EM algorithm in continuum: sparse measure solutions
• Sparse regularization on thin grids I: the Lasso
• Sampling signals with finite rate of innovation
• Sparse spikes super-resolution on thin grids II: the continuous basis pursuit
• Towards a Mathematical Theory of Super‐resolution
• Signal Recovery by Proximal Forward-Backward Splitting
• The Alternating Descent Conditional Gradient Method for Sparse Inverse Problems
• Compressed sensing
• Convergence of a block coordinate descent method for nondifferentiable minimization

This page was built for publication: On the uniqueness of solutions for the basis pursuit in the continuum