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Prior Information Guided Image Processing and Compressive Sensing

Qin, Jing
http://rave.ohiolink.edu/etdc/view?acc_num=case1365020074

Abstract Details

2013, Doctor of Philosophy, Case Western Reserve University, Applied Mathematics.
Signal/image processing and reconstruction based on mathematical modeling and computational techniques have been well developed and still attract much attention due to their broad applications. It becomes challenging to build mathematical models if the given data lacks some certainties. Prior information, including geometric priors, high frequency priors, spatially variant intensity variations and image regularities, assists to establish mathematical models by providing a more accurate description of the underlying signal/image. We have been exploring applications of the extracted prior information in two directions: integrating prior information into the image denoising explained in nonlocal means (NL-means) denoising framework; enhancing the compressive sensing signal/image reconstruction with the guidance of prior information. The first topic is geometric information based image denoising, where we develop a segmentation boosted image denoising scheme, balancing the removal of excessive noise and preservation of fine features. By virtue of segmentation algorithms and more general geometry extraction schemes, we are able to obtain the phase or geometric prior information. Based on the NL-means method, we introduce a mutual position function to ensure that averaging is only taken over pixels in the same image phase. To further improve the performance, we provide the respective selection scheme for the convolution kernel and the weight function. To address the unreliable segmentation due to the presence of excessive noise, the phase prior is relaxed to a more general geometric prior. The second topic is prior information guided compressive sensing signal/image reconstruction. Concerning the 1D signal reconstruction, we extract high frequency subbands as prior to boost the subsequent reconstruction. In 2D image reconstruction realm, we propose a novel two-stage intensity variation prior guided image reconstruction method using pixel-to-pixel varying weights associated to the total variation. By incorporating high order image regularity prior, we develop one total generalized variation (TGV) based image reconstruction model. Unlike the traditional wavelet which is only able to detect locations of singularities, shearlet transform can efficiently provide more geometric information of singularities in images, e.g. direction. Therefore we adopt the shearlet transform to boost the sparsity in image reconstruction algorithms. In addition, our work in signal/image denoising and reconstruction can be easily generalized to deal with other kinds of noise or measurements.
Weihong Guo (Advisor)
Daniela Calvetti (Committee Member)
Erkki Somersalo (Committee Member)
David Wilson (Committee Member)
186 p.
Applied Mathematics
image denoising; compressive sensing; prior information

Recommended Citations

Citations

  • Qin, J. (2013). Prior Information Guided Image Processing and Compressive Sensing [Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1365020074

    APA Style (7th edition)

  • Qin, Jing. Prior Information Guided Image Processing and Compressive Sensing. 2013. Case Western Reserve University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1365020074.

    MLA Style (8th edition)

  • Qin, Jing. "Prior Information Guided Image Processing and Compressive Sensing." Doctoral dissertation, Case Western Reserve University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=case1365020074

    Chicago Manual of Style (17th edition)

case1365020074
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© 2013, all rights reserved.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.