7,271 research outputs found
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
Wavelet transforms and their applications to MHD and plasma turbulence: a review
Wavelet analysis and compression tools are reviewed and different
applications to study MHD and plasma turbulence are presented. We introduce the
continuous and the orthogonal wavelet transform and detail several statistical
diagnostics based on the wavelet coefficients. We then show how to extract
coherent structures out of fully developed turbulent flows using wavelet-based
denoising. Finally some multiscale numerical simulation schemes using wavelets
are described. Several examples for analyzing, compressing and computing one,
two and three dimensional turbulent MHD or plasma flows are presented.Comment: Journal of Plasma Physics, 201
Einstein equations in the null quasi-spherical gauge III: numerical algorithms
We describe numerical techniques used in the construction of our 4th order
evolution for the full Einstein equations, and assess the accuracy of
representative solutions. The code is based on a null gauge with a
quasi-spherical radial coordinate, and simulates the interaction of a single
black hole with gravitational radiation. Techniques used include spherical
harmonic representations, convolution spline interpolation and filtering, and
an RK4 "method of lines" evolution. For sample initial data of "intermediate"
size (gravitational field with 19% of the black hole mass), the code is
accurate to 1 part in 10^5, until null time z=55 when the coordinate condition
breaks down.Comment: Latex, 38 pages, 29 figures (360Kb compressed
Dynamic mode decomposition in vector-valued reproducing kernel Hilbert spaces for extracting dynamical structure among observables
Understanding nonlinear dynamical systems (NLDSs) is challenging in a variety
of engineering and scientific fields. Dynamic mode decomposition (DMD), which
is a numerical algorithm for the spectral analysis of Koopman operators, has
been attracting attention as a way of obtaining global modal descriptions of
NLDSs without requiring explicit prior knowledge. However, since existing DMD
algorithms are in principle formulated based on the concatenation of scalar
observables, it is not directly applicable to data with dependent structures
among observables, which take, for example, the form of a sequence of graphs.
In this paper, we formulate Koopman spectral analysis for NLDSs with structures
among observables and propose an estimation algorithm for this problem. This
method can extract and visualize the underlying low-dimensional global dynamics
of NLDSs with structures among observables from data, which can be useful in
understanding the underlying dynamics of such NLDSs. To this end, we first
formulate the problem of estimating spectra of the Koopman operator defined in
vector-valued reproducing kernel Hilbert spaces, and then develop an estimation
procedure for this problem by reformulating tensor-based DMD. As a special case
of our method, we propose the method named as Graph DMD, which is a numerical
algorithm for Koopman spectral analysis of graph dynamical systems, using a
sequence of adjacency matrices. We investigate the empirical performance of our
method by using synthetic and real-world data.Comment: 34 pages with 4 figures, Published in Neural Networks, 201
- …