TY  - JOUR
A1  - Carpentier, Alexandra
A1  - Kim, Arlene K. H.
T1  - An iterative hard thresholding estimator for low rank matrix recovery with explicit limiting distribution
JF  - Statistica Sinica
N2  - We consider the problem of low rank matrix recovery in a stochastically noisy high-dimensional setting. We propose a new estimator for the low rank matrix, based on the iterative hard thresholding method, that is computationally efficient and simple. We prove that our estimator is optimal in terms of the Frobenius risk and in terms of the entry-wise risk uniformly over any change of orthonormal basis, allowing us to provide the limiting distribution of the estimator. When the design is Gaussian, we prove that the entry-wise bias of the limiting distribution of the estimator is small, which is of interest for constructing tests and confidence sets for low-dimensional subsets of entries of the low rank matrix.
KW  - High dimensional statistical inference
KW  - inverse problem
KW  - limiting distribution
KW  - low rank matrix recovery
KW  - numerical methods
KW  - uncertainty quantification
Y1  - 2018
U6  - https://doi.org/10.5705/ss.202016.0103
SN  - 1017-0405
SN  - 1996-8507
VL  - 28
IS  - 3
SP  - 1371
EP  - 1393
PB  - Statistica Sinica, Institute of Statistical Science, Academia Sinica
CY  - Taipei
ER  - 
TY  - GEN
A1  - Minchev, Borislav
A1  - Chambodut, Aude
A1  - Holschneider, Matthias
A1  - Panet, Isabelle
A1  - Schöll, Eckehard
A1  - Mandea, Mioara
A1  - Ramillien, Guillaume
T1  - Local multi-polar expansions in potential field modeling
T2  - Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe
N2  - The satellite era brings new challenges in the development and the implementation of potential field models. Major aspects are, therefore, the exploitation of existing space- and ground-based gravity and magnetic data for the long-term. Moreover, a continuous and near real-time global monitoring of the Earth system, allows for a consistent integration and assimilation of these data into complex models of the Earth’s gravity and magnetic fields, which have to consider the constantly increasing amount of available data. In this paper we propose how to speed up the computation of the normal equation in potential filed modeling by using local multi-polar approximations of the modeling functions. The basic idea is to take advantage of the rather smooth behavior of the internal fields at the satellite altitude and to replace the full available gravity or magnetic data by a collection of local moments. We also investigate what are the optimal values for the free parameters of our method. Results from numerical experiments with spherical harmonic models based on both scalar gravity potential and magnetic vector data are presented and discussed. The new developed method clearly shows that very large datasets can be used in potential field modeling in a fast and more economic manner.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 845 
KW  - potential fields (gravity, geomagnetism)
KW  - inverse problem
KW  - spherical harmonics
KW  - satellite data
KW  - size reduction
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-428990
SN  - 1866-8372
IS  - 845
SP  - 1127
EP  - 1141
ER  - 
TY  - JOUR
A1  - Guillemoteau, Julien
A1  - Sailhac, Pascal
A1  - Behaegel, Mickael
T1  - Modelling an arbitrarily oriented magnetic dipole over a homogeneous half-space for a rapid topographic correction of airborne EM data
JF  - Exploration geophysics : the bulletin of the Australian Society of Exploration Geophysicists
N2  - Most airborne electromagnetic (EM) processing programs assume a flat ground surface. However, in mountainous areas, the system can be at an angle with regard to the ground. As the system is no longer parallel to the ground surface, the measured magnetic field has to be corrected and the ground induced eddy current has to be modelled in a better way when performing a very fine interpretation of the data. We first recall the theoretical background for the modelling of a magnetic dipole source and study it in regard to the case of an arbitrarily oriented magnetic dipole. We show in particular how transient central loop helicopter borne data are influenced by this inclination. The result shows that the effect of topography on airborne EM is more important at early time windows and for systems using a short cut-off source. In this paper, we suggest that an estimate be made off the locally averaged inclination of the system to the ground and then to correct the data for this before inverting it (whether the inversion assumes a flat 1D, 2D or 3D sub-surface). Both 1D and 2D inversions are applied to synthetic and real data sets with such a correction. The consequence on the ground imaging is small for slopes with an angle less than 25 degrees but the correction factor can be useful for improving the estimation of depths in mountainous areas.
KW  - airborne geophysics
KW  - electromagnetic imaging
KW  - inverse problem
Y1  - 2015
U6  - https://doi.org/10.1071/EG13093
SN  - 0812-3985
SN  - 1834-7533
VL  - 46
IS  - 1
SP  - 85
EP  - 96
PB  - CSIRO
CY  - Clayton
ER  -