We propose two new approaches for efficiently compressing unstructured data defined on the unit sphere. Both approaches are based upon a meshfree multiscale representation of functions on the unit sphere. This multiscale representation employs compactly supported radial basis functions of different scales. The first approach is based on a simple thresholding strategy after the multiscale repres...

We compare two state-of-the-art non-linear techniques for nonparametric function estimation via piecewise constant approximation: the taut string and the Unbalanced Haar methods. While it is well-known that the latter is multiscale, it is not obvious that the former can also be interpreted as multiscale. We provide a unified multiscale representation for both methods, which offers an insight in...

We propose a generalized multiscale finite element method (GMsFEM) based on clustering algorithm to study the elliptic PDEs with random coefficients in the multiquery setting. Our method consists of offline and online stages. In the offline stage, we construct a small number of reduced basis functions within each coarse grid block, which can then be used to approximate the multiscale finite ele...

Cardiovascular signals are largely analyzed using traditional time and frequency domain measures. However, such measures fail to account for important properties related to multiscale organization and non-equilibrium dynamics. The complementary role of conventional signal analysis methods and emerging multiscale techniques, is, therefore, an important frontier area of investigation. The key fin...

The Green's function of the Poisson equation, and its spatial derivatives, lead to a family of wavelets specifically tailored to potential fields. Upward continuation of the field is seen to be identical to these wavelets' scale change operation. The maxima at all heights of the field's horizontal gradients are termed the field's multiscale edges. A multiscale edge's field strength variation an...

The thesis provides a detailed analysis of the independence structure possessed by multiscale models and demonstrates that such an analysis provides important insight into the multiscale stochastic realization problem. Multiscale models constitute a broad class of probabilistic models which includes the well-known subclass of multiscale autoregressive (MAR) models. MAR models have proven useful...

In this survey paper, we overview the various network traffic models, especially focusing on the multiscale analysis. By multiscale analysis we mean wavelet-based self-similar and multifractal analysis. Multiscale analysis is advantageous in that it can reveal the scaling behavior of the traffic on large time scale, at the same time characterize small-scale irregularity. We also discuss how we ...

This paper introduces a new way of extracting affine invariant features from image functions. The presented approach is based on combining affine moment invariants (AMI) with multiscale invariants, in particular multiscale autoconvolution (MSA) and spatial multiscale affine invariants (SMA). Our approach includes all of these invariants as special cases, but also makes it possible to construct ...

This research is concerned with next-generation multiscale data assimilation, with a focus on shelfbreak regions, including non-hydrostatic effects. Our long-term goals are to: Develop and utilize GMM-DO data assimilation schemes for rigorous multiscale inferences, where observations provide information on varied spatial and temporal scales Develop and utilize test cases and simulation experime...

This research is concerned with next-generation multiscale data assimilation, with a focus on shelfbreak regions, including non-hydrostatic effects. Our long-term goals are to: Develop and utilize GMM-DO data assimilation schemes for rigorous multiscale inferences, where observations provide information on varied spatial and temporal scales Develop and utilize test cases and simulation experime...