Publications related to Nonideal sampling and regularized interpolation of noisy data

Sparsity-Driven Statistical Inference for Inverse Problems

This thesis addresses statistical inference for the resolution of inverse problems. Our work is motivated by the recent trend whereby classical linear methods are being replaced by nonlinear alternatives that rely on the sparsity of naturally occurring sig ...

EPFL2015

Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

Fabio Nobile, Giovanni Migliorati

We study the accuracy of the discrete least-squares approximation on a finite-dimensional space of a real-valued target function from noisy pointwise evaluations at independent random points distributed according to a given sampling probability measure. Th ...

2015

MATHICSE Technical Report : Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

Fabio Nobile, Giovanni Migliorati

We study the accuracy of the discrete least-squares approximation on a finite dimensional space of a real-valued target function from noisy pointwise evaluations at independent random points distributed according to a given sampling probability measure. Th ...

MATHICSE2015

A New Estimation Algorithm for the GNSS-R Interference Pattern Technique: The Segmented Maximum-Likelihood

Pierre-André Farine, Cyril Botteron, Miguel Angel Ribot Sanfelix

During the last years, Global Navigation Satellite Systems (GNSS) reflectometry (GNSS-R) receivers have proven in several field experiments that GNSS signals reflected and scattered from the Earth’s surface can be used in passive remote sensing application ...

2015

Statistical Optimality of Hermite Splines

Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann, Harshit Gupta

Hermite splines are commonly used for interpolating data when samples of the derivative are available, in a scheme called Hermite interpolation. Assuming a suitable statistical model, we demonstrate that this method is actually optimal for reconstructing r ...

IEEE2015

Sparsistency of $\ell_1$-Regularized $M$-Estimators

Volkan Cevher, Jonathan Mark Scarlett, Yen-Huan Li

We consider the model selection consistency or sparsistency of a broad set of

\ell_1

-regularized

M

-estimators for linear and non-linear statistical models in a unified fashion. For this purpose, we propose the local structured smoothness condition (LSS ...

2015

Multitask diffusion LMS with sparsity-based regularization

Ali H. Sayed, Roula Nassif

In this work, a diffusion-type algorithm is proposed to solve multitask estimation problems where each cluster of nodes is interested in estimating its own optimum parameter vector in a distributed manner. The approach relies on minimizing a global mean-sq ...

IEEE2015

Total Variation Regularization of Shape Signals

Martin Kurt Storath

This paper introduces the concept of shape signals, i.e., series of shapes which have a natural temporal or spatial ordering, as well as a variational formulation for the regularization of these signals. The proposed formulation can be seen as the shape-va ...

IEEE2015

A Modulated Closed Form solution for Quantitative Susceptibility Mapping - A thorough evaluation and comparison to iterative methods based on edge prior knowledge

Rolf Gruetter, Yves Wiaux, José Pedro Rebelo Ferreira Marques, Diana Khabipova

The aim of this study is to perform a thorough comparison of quantitative susceptibility mapping (QSM) techniques and their dependence on the assumptions made. The compared methodologies were: two iterative single orientation methodologies minimizing the l ...

Elsevier2015

Time–Data Tradeoffs by Aggressive Smoothing

Volkan Cevher

This paper proposes a tradeoff between sample complexity and computation time that applies to statistical estimators based on convex optimization. As the amount of data increases, we can smooth optimization problems more and more aggressively to achieve ac ...

2014

Nonideal sampling and regularized interpolation of noisy data

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Sparsity-Driven Statistical Inference for Inverse Problems

Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

MATHICSE Technical Report : Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

A New Estimation Algorithm for the GNSS-R Interference Pattern Technique: The Segmented Maximum-Likelihood

Statistical Optimality of Hermite Splines

Sparsistency of $\ell_1$-Regularized $M$-Estimators

Multitask diffusion LMS with sparsity-based regularization

Total Variation Regularization of Shape Signals

A Modulated Closed Form solution for Quantitative Susceptibility Mapping - A thorough evaluation and comparison to iterative methods based on edge prior knowledge

Time–Data Tradeoffs by Aggressive Smoothing

Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

MATHICSE Technical Report : Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

Multitask diffusion LMS with sparsity-based regularization

Statistical Optimality of Hermite Splines

A Modulated Closed Form solution for Quantitative Susceptibility Mapping - A thorough evaluation and comparison to iterative methods based on edge prior knowledge

Total Variation Regularization of Shape Signals

A New Estimation Algorithm for the GNSS-R Interference Pattern Technique: The Segmented Maximum-Likelihood

Sparsistency of $\ell_1$-Regularized $M$-Estimators

Sparsity-Driven Statistical Inference for Inverse Problems

Time–Data Tradeoffs by Aggressive Smoothing