44 research outputs found
A Multilevel Monte Carlo Estimator for Matrix Multiplication
Inspired by the latest developments in multilevel Monte Carlo (MLMC) methods
and randomised sketching for linear algebra problems we propose a MLMC
estimator for real-time processing of matrix structured random data. Our
algorithm is particularly effective in handling high-dimensional inner products
and matrix multiplication, in applications of image analysis and large-scale
supervised learning.Comment: 23 pages, 3 figure
Imaging of atmospheric dispersion processes with Differential Absorption Lidar
We consider the inverse problem of fitting atmospheric dispersion parameters
based on time-resolved back-scattered differential absorption Lidar (DIAL)
measurements. The obvious advantage of light-based remote sensing modalities is
their extended spatial range which makes them less sensitive to strictly local
perturbations/modelling errors or the distance to the plume source. In contrast
to other state-of-the-art DIAL methods, we do not make a single scattering
assumption but rather propose a new type modality which includes the collection
of multiply scattered photons from wider/multiple fields-of-view and argue that
this data, paired with a time dependent radiative transfer model, is beneficial
for the reconstruction of certain image features. The resulting inverse problem
is solved by means of a semi-parametric approach in which the image is reduced
to a small number of dispersion related parameters and high-dimensional but
computationally convenient nuisance component. This not only allows us to
effectively avoid a high-dimensional inverse problem but simultaneously
provides a natural regularisation mechanism along with parameters which are
directly related to the dispersion model. These can be associated with
meaningful physical units while spatial concentration profiles can be obtained
by means of forward evaluation of the dispersion process
High-order regularized regression in Electrical Impedance Tomography
We present a novel approach for the inverse problem in electrical impedance
tomography based on regularized quadratic regression. Our contribution
introduces a new formulation for the forward model in the form of a nonlinear
integral transform, that maps changes in the electrical properties of a domain
to their respective variations in boundary data. Using perturbation theory the
transform is approximated to yield a high-order misfit unction which is then
used to derive a regularized inverse problem. In particular, we consider the
nonlinear problem to second-order accuracy, hence our approximation method
improves upon the local linearization of the forward mapping. The inverse
problem is approached using Newton's iterative algorithm and results from
simulated experiments are presented. With a moderate increase in computational
complexity, the method yields superior results compared to those of regularized
linear regression and can be implemented to address the nonlinear inverse
problem