TV-based spline reconstruction with Fourier measurements: uniqueness and convergence of grid-based methods
DOI10.1016/j.cam.2022.114937zbMath1504.94032arXiv2202.05059OpenAlexW4308930804MaRDI QIDQ2104103
Thomas Debarre, Quentin Denoyelle, Julien Fageot
Publication date: 9 December 2022
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2202.05059
optimizationsplinesinverse problemsFourier analysisgeneralized total-variation regularizationgrid-based algorithms
Convex programming (90C25) Numerical optimization and variational techniques (65K10) Classical almost periodic functions, mean periodic functions (42A75) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Spline approximation (41A15)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
- Nonlinear total variation based noise removal algorithms
- 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
- Spline solutions to L\(^1\) extremal problems in one and several variables
- A practical guide to splines
- A theory of super-resolution from short-time Fourier transform measurements
- Sparsest piecewise-linear regression of one-dimensional data
- On the linear convergence rates of exchange and continuous methods for total variation minimization
- Sparsity of solutions for variational inverse problems with finite-dimensional data
- Spike detection from inaccurate samplings
- Splines Are Universal Solutions of Linear Inverse Problems with Generalized TV Regularization
- Continuous-Domain Solutions of Linear Inverse Problems With Tikhonov Versus Generalized TV Regularization
- Periodic Splines and Gaussian Processes for the Resolution of Linear Inverse Problems
- Inverse problems in spaces of measures
- Multikernel Regression with Sparsity Constraint
- Exact solutions of infinite dimensional total-variation regularized problems
- On the uniqueness of solutions for the basis pursuit in the continuum
- TV-based reconstruction of periodic functions
- A fast homotopy algorithm for gridless sparse recovery
- Pocket guide to solve inverse problems with GlobalBioIm
- The sliding Frank–Wolfe algorithm and its application to super-resolution microscopy
- B-Spline-Based Exact Discretization of Continuous-Domain Inverse Problems With Generalized TV Regularization
- On Representer Theorems and Convex Regularization
- Hybrid-Spline Dictionaries for Continuous-Domain Inverse Problems
- Sparse regularization on thin grids I: the Lasso
- Sparse spikes super-resolution on thin grids II: the continuous basis pursuit
- Towards a Mathematical Theory of Super‐resolution
- Convex Analysis
- The Alternating Descent Conditional Gradient Method for Sparse Inverse Problems
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