Heat kernel generated frames in the setting of Dirichlet spaces
T Coulhon, G Kerkyacharian, P Petrushev - Journal of Fourier Analysis and …, 2012 - Springer
Wavelet bases and frames consisting of band limited functions of nearly exponential
localization on ℝ d are a powerful tool in harmonic analysis by making various spaces of …
localization on ℝ d are a powerful tool in harmonic analysis by making various spaces of …
Efficient Nonparametric Bayesian Inference For X-Ray Transforms
We consider the statistical inverse problem of recovering a function f: M→ ℝ, where M is a
smooth compact Riemannian manifold with boundary, from measurements of general X-ray …
smooth compact Riemannian manifold with boundary, from measurements of general X-ray …
A variational view on statistical multiscale estimation
We present a unifying view on various statistical estimation techniques including
penalization, variational, and thresholding methods. These estimators are analyzed in the …
penalization, variational, and thresholding methods. These estimators are analyzed in the …
Localized spherical deconvolution
G Kerkyacharian, TM Pham Ngoc, D Picard - 2011 - projecteuclid.org
Localized spherical deconvolution Page 1 The Annals of Statistics 2011, Vol. 39, No. 2,
1042–1068 DOI: 10.1214/10-AOS858 © Institute of Mathematical Statistics, 2011 LOCALIZED …
1042–1068 DOI: 10.1214/10-AOS858 © Institute of Mathematical Statistics, 2011 LOCALIZED …
Shape-constrained regularization by statistical multiresolution for inverse problems: asymptotic analysis
K Frick, P Marnitz, A Munk - Inverse Problems, 2012 - iopscience.iop.org
This paper is concerned with a novel regularization technique for solving linear ill-posed
operator equations in Hilbert spaces from data that are corrupted by white noise. We …
operator equations in Hilbert spaces from data that are corrupted by white noise. We …
Adaptive estimation in the nonparametric random coefficients binary choice model by needlet thresholding
E Gautier, E Le Pennec - 2018 - projecteuclid.org
In the random coefficients binary choice model, a binary variable equals 1 iff an index X^⊤β
is positive. The vectors X and β are independent and belong to the sphere S^d-1 in R^d. We …
is positive. The vectors X and β are independent and belong to the sphere S^d-1 in R^d. We …
[HTML][HTML] Confidence regions for images observed under the Radon transform
N Bissantz, H Holzmann, K Proksch - Journal of Multivariate Analysis, 2014 - Elsevier
Recovering a function f from its integrals over hyperplanes (or line integrals in the two-
dimensional case), that is, recovering f from the Radon transform R f of f, is a basic problem …
dimensional case), that is, recovering f from the Radon transform R f of f, is a basic problem …
Blockwise SVD with error in the operator and application to blind deconvolution
S Delattre, M Hoffmann, D Picard, T Vareschi - 2012 - projecteuclid.org
We consider linear inverse problems in a nonparametric statistical framework. Both the
signal and the operator are unknown and subject to error measurements. We establish …
signal and the operator are unknown and subject to error measurements. We establish …
Testing the isotropy of high energy cosmic rays using spherical needlets
G Faÿ, J Delabrouille, G Kerkyacharian… - The Annals of Applied …, 2013 - JSTOR
For many decades, ultrahigh energy charged particles of unknown origin that can be
observed from the ground have been a puzzle for particle physicists and astrophysicists. As …
observed from the ground have been a puzzle for particle physicists and astrophysicists. As …