We consider in this thesis the statistical linear inverse problem $Y = Af+ \epsilon \xi$ where $A$ denotes a compact operator, $\epsilon>0$ a noise level and $\xi$ a Gaussian white noise. The unknown function f has to be recovered from the indirect measurement Y . Given a family $\Lambda$, an oracle inequality compares the performances of an adaptive estimator $f^{\star}$ to the best one in $\Lambda$. Such an inequality is non-asymptotic and no specific informations on $f$ are required. In this thesis, we propose different oracle inequalities in order to provide both a better understanding of regularization with a noisy operator and ageneralization of the risk hull minimization (RHM) algorithm. For most of the existing methods, the operator...
We consider statistical linear inverse problems in Hilbert spaces of the type ˆ Y = Kx + U where we ...
This paper deals with recovering an unknown vector θ from the noisy data Y = Aθ + σξ, where A is a k...
This thesis is concerned with recovery guarantees and sensitivity analysis of variational regulariza...
We consider in this thesis the statistical linear inverse problem $Y = Af+ \epsilon \xi$ where $A$ d...
International audienceWe consider in this paper the statistical linear inverse problem $Y=Af+\epsilo...
We consider the statistical inverse problem to recover f from noisy measurements Y = Tf + sigma xi w...
International audienceWe are interested in the statistical linear inverse problem $ Y=Af+\epsilon \x...
This thesis focuses on the impact of the imprecision on a linear operator when the latter is at stak...
We tackle the problem of estimating a regression function observed in an instrumental regression fra...
In this thesis, we study some aspects of the non-parametric regression functions estimation. Our pro...
International audienceIn this paper, we aim at recovering an unknown signal x0 from noisy L1measurem...
À partir des observations Z(n) = {(Xi, Yi), i = 1, ..., n} satisfaisant Yi = f(Xi) + ζi, nous voulon...
This thesis is concerned with recovery guarantees and sensitivity analysis of variational regulariza...
Abstract. We consider the problem of estimating an unknown vector θ from the noisy data Y = Aθ + ǫ, ...
International audienceIn this paper, we propose two algorithms to solve a large class of linear inve...
We consider statistical linear inverse problems in Hilbert spaces of the type ˆ Y = Kx + U where we ...
This paper deals with recovering an unknown vector θ from the noisy data Y = Aθ + σξ, where A is a k...
This thesis is concerned with recovery guarantees and sensitivity analysis of variational regulariza...
We consider in this thesis the statistical linear inverse problem $Y = Af+ \epsilon \xi$ where $A$ d...
International audienceWe consider in this paper the statistical linear inverse problem $Y=Af+\epsilo...
We consider the statistical inverse problem to recover f from noisy measurements Y = Tf + sigma xi w...
International audienceWe are interested in the statistical linear inverse problem $ Y=Af+\epsilon \x...
This thesis focuses on the impact of the imprecision on a linear operator when the latter is at stak...
We tackle the problem of estimating a regression function observed in an instrumental regression fra...
In this thesis, we study some aspects of the non-parametric regression functions estimation. Our pro...
International audienceIn this paper, we aim at recovering an unknown signal x0 from noisy L1measurem...
À partir des observations Z(n) = {(Xi, Yi), i = 1, ..., n} satisfaisant Yi = f(Xi) + ζi, nous voulon...
This thesis is concerned with recovery guarantees and sensitivity analysis of variational regulariza...
Abstract. We consider the problem of estimating an unknown vector θ from the noisy data Y = Aθ + ǫ, ...
International audienceIn this paper, we propose two algorithms to solve a large class of linear inve...
We consider statistical linear inverse problems in Hilbert spaces of the type ˆ Y = Kx + U where we ...
This paper deals with recovering an unknown vector θ from the noisy data Y = Aθ + σξ, where A is a k...
This thesis is concerned with recovery guarantees and sensitivity analysis of variational regulariza...