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We show that measures with finite support on the real line are the unique solution to an algorithm, named generalized minimal extrapolation, involving only a finite number of generalized moments (which encompass the standard moments, the Laplace transform, the Stieltjes transformation, etc). Generalized minimal extrapolation shares related geometric… (More)

We investigate the multi-dimensional Super Resolution problem on closed semi-algebraic domains for various sampling schemes such as Fourier or moments. We present a new semidefinite programming (SDP) formulation of the 1-minimization in the space of Radon measures in the multi-dimensional frame on semi-algebraic sets. While standard approaches have focused… (More)

This article investigates a new parameter for the high-dimensional regression with noise: the distortion. This latter has attracted a lot of attention recently with the appearance of new deterministic constructions of " almost "-Euclidean sections of the L1-ball. It measures how far is the intersection between the kernel of the design matrix and the unit… (More)

Restricted Isometry Constants (RICs) are a pivotal notion in Compressed Sensing (CS) as these constants finely assess how a linear operator is conditioned on the set of sparse vectors and hence how it performs in stable and robust sparse regression (SRSR). While it is an open problem to construct deterministic matrices with apposite RICs, one can prove that… (More)

In this paper, we aim at recovering an undirected weighted graph of N vertices from the knowledge of a perturbed version of the eigenspaces of its adjacency matrix W. Our approach is based on minimizing a cost function given by the Frobenius norm of the commutator AB−BA between symmetric matrices A and B. In the Erdős-Rényi model with no self-loops, we show… (More)

In this paper, we study sparse spike deconvolution over the space of complex-valued measures when the input measure is a finite sum of Dirac masses. We introduce a modified version of the Beurling Lasso (BLasso), a semi-definite program that we refer to as the Concomitant Beurling Lasso (CBLasso). This new procedure estimates the target measure and the… (More)

This article investigates deterministic design matrices X for the fundamental problems of error prediction and variable selection given observations y = Xβ ⋆ + z where z is a stochastic error term. In this paper, deterministic design matrices are derived from unbalanced expander graphs, and we show that it is possible to accurately estimate the prediction… (More)

In this article we show that measures, with finite support on the real line, are the unique solution to an algorithm, named support pursuit, involving only a finite number of generalized moments (which encompass the standard moments, the Laplace transform, the Stieljes transformation, etc...). The support pursuit share related geometric properties with… (More)

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