Image Deblurring and Decomposition: Texture and Color Image Analysis

  • Kang, Sung (PI)

Grants and Contracts Details


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.
Effective start/end date9/1/078/31/08


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