Angular super-resolution retrieval in small-angle X-ray scattering.

Small-angle X-ray scattering (SAXS) techniques enable convenient nanoscopic characterization for various systems and conditions. Unlike synchrotron-based setups, lab-based SAXS systems intrinsically suffer from lower X-ray flux and limited angular resolution. Here, we develop a two-step retrieval methodology to enhance the angular resolution for given experimental conditions.

Accelerating Particle Filter Using Randomized Multiscale and Fast Multipole Type Methods.

Particle filter is a powerful tool for state tracking using non-linear observations. We present a multiscale based method that accelerates the tracking computation by particle filters. Unlike the conventional way, which calculates weights over all particles in each cycle of the algorithm, we sample a small subset from the source particles using matrix decomposition methods.

Nonuniform sampling, image recovery from sparse data and the discrete sampling theorem.

In many applications, sampled data are collected in irregular fashion or are partly lost or unavailable. In these cases, it is necessary to convert irregularly sampled signals to regularly sampled ones or to restore missing data. We address this problem in the framework of a discrete sampling theorem for band-limited discrete signals that have a limited number of nonzero transform coefficients in a certain transform domain.