B-Spline-Based Exact Discretization of Continuous-Domain Inverse Problems With Generalized TV Regularization
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The goal of this thesis is to study continuous-domain inverse problems for the reconstruction of sparse signals and to develop efficient algorithms to solve such problems computationally. The task is to recover a signal of interest as a continuous function ...
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We focus on the generalized-interpolation problem. There, one reconstructs continuous-domain signals that honor discrete data constraints. This problem is infinite-dimensional and ill-posed. We make it well-posed by imposing that the solution balances data ...
We study 1D continuous-domain inverse problems for multicomponent signals. The prior assumption on these signals is that each component is sparse in a different dictionary specified by a regularization operators. We introduce a hybrid regularization functi ...
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We present and analyze a novel wavelet-Fourier technique for the numerical treatment of multidimensional advection–diffusion–reaction equations based on the COmpRessed SolvING (CORSING) paradigm. Combining the Petrov–Galerkin technique with the compressed ...
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We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is formulated as a penalized convex optimization problem, taking the form of a sum ...
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In inverse problems, the task is to reconstruct an unknown signal from its possibly noise-corrupted measurements. Penalized-likelihood-based estimation and Bayesian estimation are two powerful statistical paradigms for the resolution of such problems. They ...
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We propose a discretization method for continuous-domain linear inverse problems with multiple-order total-variation (TV) regularization. It is based on a recent result that proves that such inverse problems have sparse polynomial-spline solutions. Our met ...
IEEE2019
, , ,
We propose a discretization method for continuous-domain linear inverse problems with multiple-order total-variation (TV) regularization. It is based on a recent result that proves that such inverse problems have sparse polynomial-spline solutions. Our met ...
