Variational Methods For Continuous-Domain Inverse Problems: the Quest for the Sparsest Solution
TJ Debarre - 2022 - infoscience.epfl.ch
… Our discretization method is again motivated by our multicomponent representer theorem
which guarantees that such problems admit a solution that is a hybrid spline, ie, the sum of a L1…
which guarantees that such problems admit a solution that is a hybrid spline, ie, the sum of a L1…
Continuous-domain formulation of inverse problems for composite sparse-plus-smooth signals
… Therefore, when feasible, to formulate the inverse problem in the continuous domain is a …
) to 1D continuous-domain composite signals by solving an optimization problem of the form …
) to 1D continuous-domain composite signals by solving an optimization problem of the form …
Optimization Over Banach Spaces: A Unified View on Supervised Learning and Inverse Problems
S Aziznejad - 2022 - infoscience.epfl.ch
… In this thesis, we focus on continuous-domain linear inverse problems with finitely many
observations … Unser, “Hybrid-spline dictionaries for continuousdomain inverse problems,” IEEE …
observations … Unser, “Hybrid-spline dictionaries for continuousdomain inverse problems,” IEEE …
Coupled splines for sparse curve fitting
… Abstract—We formulate as an inverse problem the construction … We prove that an optimal
solution to the inverse problem is a … , “Hybrid-spline dictionaries for continuous-domain inverse …
solution to the inverse problem is a … , “Hybrid-spline dictionaries for continuous-domain inverse …
[PDF][PDF] On the Uniqueness of Inverse Problems with Fourier-domain Measurements and Generalized TV Regularization
… This paper deals with continuous-domain inverse problems, where the goal is to recover a
periodic … Unser, “Hybrid-spline dictionaries for continuous-domain inverse problems,” IEEE …
periodic … Unser, “Hybrid-spline dictionaries for continuous-domain inverse problems,” IEEE …
[PDF][PDF] Sparsest continuous piecewise-linear representation of data
… However, contrary to CNNs, we formulate the learning problem as a regularized inverse
problem in a continuous domain framework. Our metric for model simplicity is sparsity, ie, the …
problem in a continuous domain framework. Our metric for model simplicity is sparsity, ie, the …
Sampling and reconstruction of sparse signals in shift-invariant spaces: Generalized Shannon's theorem meets compressive sensing
… We show that the continuous-domain inverse problem can … inverse problem. The proposed
framework encompasses a … are sparse in a certain dictionary. Even though the proposed …
framework encompasses a … are sparse in a certain dictionary. Even though the proposed …
Single-pixel compressive imaging in shift-invariant spaces via exact wavelet frames
… as filtering of the observed signal with continuous-domain functions that lie in an SI subspace
… of an inherently continuous-domain inverse problem to a finite-dimensional problem of CS …
… of an inherently continuous-domain inverse problem to a finite-dimensional problem of CS …
Sparsest univariate learning models under Lipschitz constraint
… , we propose continuous-domain formulations for one-dimensional regression problems.
In … -of-theart for image classification [16], inverse problems [17], and image segmentation [18]. …
In … -of-theart for image classification [16], inverse problems [17], and image segmentation [18]. …
Compressed data separation via unconstrained -split analysis
M Gu, S Li, J Lin - Analysis and Applications, 2023 - World Scientific
… We investigate the problems of reconstruction signals’ distinct subcomponents, that are …
Unser, Hybrid-spline dictionaries for continuousdomain inverse problems, IEEE Trans. …
Unser, Hybrid-spline dictionaries for continuousdomain inverse problems, IEEE Trans. …