Grants and Contracts Details
Description
One of recent developments of mathematical image
processing is the introduction of G-norm by Meyer, which opened the door
for handling texture and oscillations. There are numerous works for grayscale
image decomposition, and the PI proposes to further investigate the
color image decomposition. The PI previously studied the image decomposition
model for color image, via defining the G-norm for color image as the
polar semi norm associated to the 3D total variation semi norm. One goal
of this project is to explore more sophisticated color models, namely Chromaticity
and Brightness (CB), HSV, and vectorial RGB models for color
texture decomposition functional, and investigate better texture spaces such
as div(BMO) and homogeneous besov space for color images. Secondly,the
PI will explore blind deconvolution for texture images. The challenge there
is to correctly capture the texture in the blurry image. The PI proposes to
investigate different possibilities of the modeling G-norm as well as tackle
various computational issues. The main goal is to study blind deconvolution
in combination with image decomposition techniques. Finally, extending the
previously proposed tasks, the PI will examinecolor image deblurring and
color texture blind deconvolution. The PI proposes to consider color models
such as CB, HSV and RGB in combination with variational deblurring
techniques, and further add texture G-norm for color image deblurring.
Intellectual Merit and Broader Impacts: These proposed tasks will
advance deblurring techniques and promote basic understanding of textured
and colored image. It will provide theoretical background for methodologies
and can be applied to solve real imaging problems arising from digital
photo restorations, medical imaging, communications, information science,
and many other applications. The proposed work will involve international
collaborations with J.-F. Aujol at ENS Cachan (France), and R. March at
Rome (Italy) as well as domestic collaboration with S. Levine (Duquesne
University) and J. Shen (U. of Minnesota). On the educational aspect,
the PI will incorporate new research development in the courses offered for
graduate students in math and engineering. The PI has graduated a Ph.D.
student recently and these funded activities will help to attract new doctoral
students in this research area.
Status | Finished |
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Effective start/end date | 9/1/07 → 8/31/08 |
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