Reconstruction of Photospheric Velocity Fields from Highly Corrupted Data

Exact Recovery of Chaotic Systems from Highly Corrupted Data

Learning the governing equations in dynamical systems from time-varying measurements is of great interest across different scientific fields. This task becomes prohibitive when such data is moreover highly corrupted, for example, due to the recording mechanism failing over unknown intervals of time. When the underlying system exhibits chaotic behavior, such as sensitivity to initial conditions,...

MR Image Reconstruction from Sparse and Corrupted k-Space Data

This paper reviews resampling of nonuniformly sampled k-space data to a Cartesian grid and adds a new formula enabling quick computation of the shape parameter B of the KaiserBessel convolution window. In addition, a very recently conceived iterative estimation of the sampling density correction is explained and applied to sparse radial MRI scans. Keywords— rapid scanning, undersampling, griddi...

Image Reconstruction from Incomplete Data

Image Reconstruction from Incomplete Data

Reconstruction of large-scale peculiar velocity fields

A reconstruction method for recovering the initial conditions of the Universe starting from the present galaxy distribution is presented which guarantees uniqueness of solutions. We show how our method can be used to obtain the peculiar velocities of a large number of galaxies, hence trace galaxies orbits back in time and obtain the entire past dynamical history of the Universe above scales whe...