@article{GuillemoteauSailhacBehaegel2015,
  author    = {Guillemoteau, Julien and Sailhac, Pascal and Behaegel, Mickael},
  title     = {Modelling an arbitrarily oriented magnetic dipole over a homogeneous half-space for a rapid topographic correction of airborne EM data},
  series = {Exploration geophysics : the bulletin of the Australian Society of Exploration Geophysicists},
  volume    = {46},
  journal   = {Exploration geophysics : the bulletin of the Australian Society of Exploration Geophysicists},
  number    = {1},
  publisher = {CSIRO},
  address   = {Clayton},
  issn      = {0812-3985},
  doi       = {10.1071/EG13093},
  pages     = {85 -- 96},
  year      = {2015},
  abstract  = {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.},
  language  = {en}
}
@article{CarpentierKim2018,
  author    = {Carpentier, Alexandra and Kim, Arlene K. H.},
  title     = {An iterative hard thresholding estimator for low rank matrix recovery with explicit limiting distribution},
  series = {Statistica Sinica},
  volume    = {28},
  journal   = {Statistica Sinica},
  number    = {3},
  publisher = {Statistica Sinica, Institute of Statistical Science, Academia Sinica},
  address   = {Taipei},
  issn      = {1017-0405},
  doi       = {10.5705/ss.202016.0103},
  pages     = {1371 -- 1393},
  year      = {2018},
  abstract  = {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.},
  language  = {en}
}