Research at Present
Multiscale Methods for Geopotential
Modeling
Compressed Sensing and its
Applications
Statistical Analysis of High-Resolution fMRI
Image Processing Schemes for
Brushstroke Analysis of van GoghÕs Paintings
Reproducible Research
Multiscale
Methods for Geopotential Modeling
An inertial
navigation system (INS) is a device which provides the position, velocities and
attitude of an aircraft or vehicle. INS determines the local gravity vector
using a gravity model and integrates the specific force data over time to
obtain vehicle velocity and position. Navigating platforms need accurate
gravity data to meet their INS specifications. The national
Geospatial-intelligence Agency (NGA) provides customized gravity products for
US future needs. NGA is responsible for collecting, processing, and evaluating gravity
data. These data are used to compute mean gravity anomalies, geoid heights,
deflections of the vertical, and gravity disturbances. If left uncompensated,
the small gravity deflections accumulate to very large navigations errors.
Spherical
Harmonics representation is todayÕs dominant approach to geopotential modeling.
However such representation is global. In other words, by collecting even one
single gravimetric measurement, the entire representation needs to be updated.
Also, evaluating a gravimetric quantity at a single point requires accessing
all the coefficients of such global system (The most recent model has more than
4 million coefficients). Both the update and evaluation task using this system
demands extremely heavy computations. We are developing a new class of ÒlocalizedÓ
multiscale (wavelet) representations for geopotential data. Mathematical
results show that the new representations have compelling advantages over
traditional spherical harmonic approaches. We have developed software tools
specifically tailored to allow demonstration of these advantages (computational
efficiency and speed, accuracy, code complexity and nice statistical
properties). Using this new class of representation, several differential and
integral operators required to calculate gravimetric quantities are implemented
significantly more efficient.
In
our developed machinery, we have used HEALPix parameterization on the sphere which is spherical harmonics
friendly (hence fully compatible to the classical system) and is intrinsically
multiscale (hence appropriate for multiscale representation).
Compressed
Sensing (CS) and its Applications
CS
framework deals with signals which are sparse in some transform domain and can be
reconstructed with fewer (non-adaptive) samples than the standard rate (i.e rate at least twice its highest
frequency). The reconstructed signal is computed via
solving for the sparsest transform coefficients.
Compressed
sensing can be applied to many settings in imaging and signal processing
settings such as fast MR imaging, NMR spectroscopy, wireless sensor networks and optical imaging
systems. We are particularly interested in exploring how CS machinery can improve
performance of NMR spectroscopy.
Typical
NMR spectroscopy signal consist of few bumps with varying locations and
amplitudes and expected to have sparse representation in wavelet domain.
According
to the theory of CS, certain number of measurements (fewer than standard
scheme) can convey enough information for a faithful reconstruction.
Statistical
Analysis of High-Resolution fMRI
In
transition-band SSFP fMRI, the functional contrast originates from the bulk
frequency shift caused by the deoxygenated hemoglobin concentration change in
the activated brain regions. This frequency shift results in a magnitude and
phase signal change. In early low-resolution studies, only the magnitude of the
acquired signal was used to detect activation.
We
propose a complex domain data analysis framework to appropriately incorporate
phase activation information. The results show significant phase signal changes
in a large number of voxels comparable to that of the magnitude-activated
voxels. The complex analysis method successfully includes these phase
activations into the activation map, providing wider coverage compared to the
magnitude analysis results.
Image Processing Schemes for
Brushstroke Analysis of van GoghÕs Paintings
Together
with a team of art historians and image analysts, we have been developing image
processing tools to the problem of recognizing and distinguishing brushstrokes
in paintings. We apply our
methods
to paintings by van Gogh, whose broad, powerful brushstrokes fall into several
distinct categories. One of the main goals of this project is to assist art
historians in artist identification.
ÒAn
article about computational science in a scientific publication is not the
scholarship itself, it is merely advertising of the scholarship. The actual
scholarship is the complete software development environment and the complete
set of instructions which generated the figures.Ó
SphereLab