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Dissertation_Beverly_Grunden.pdf (9.47 MB)

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On the Characteristics of a Data-driven Multi-scale Frame Convergence Algorithm

Grunden, Beverly K.
http://orcid.org/0000-0002-3088-2601
http://rave.ohiolink.edu/etdc/view?acc_num=wright1622208959661057

Abstract Details

2021, Doctor of Philosophy (PhD), Wright State University, Interdisciplinary Applied Science and Mathematics PhD.
In recent years, data-driven representation methods have been introduced to improve compressed sensing image reconstruction. This research explores a recently proposed algorithm that utilizes a data-driven multi-scale Parseval frame for image compression. Because a sensing matrix by itself may be insufficient to obtain a sparse representation for an image, a frame is combined with the compressed sensing matrix to increase flexibility in obtaining a sparse representation. The two-step algorithm optimizes the representation by alternating between adjusting a sparse coefficient vector and tuning a small filterbank which determines the frame. The structure of the frame and its relationship with the underlying filterbank were examined. Numerical experiments to characterize the algorithm include a search for the appropriate regularization parameters that control emphasis between the two terms of the objective function, examination of the effect of image size, a parameter sweep of the relaxation factor of the Weak Matching Pursuit function in the first step of the algorithm, and the relaxation of the Parseval constraint in the second step. Performance metrics used to assess the numerical results include execution time and number of loops to reach convergence, sparsity of the representation, and two image quality measures – peak signal to noise ratio (PSNR) and Structural Similarity (SSIM). The experiments indicated the algorithm takes a very long time to reach convergence, even for images of moderate size, and that reconstructions will result in greater accuracy on image patches with a small number of pixels (fewer than 100). It was also found that algorithm performance varies depending on the image format used to specify image brightness of the pixels. Finally, the Parseval constraint could be removed from the algorithm with improvement in execution time and sparsity, but without loss of accuracy.
Travis J. Bemrose, Ph.D. (Committee Co-Chair)
Jason Deibel, Ph.D. (Committee Co-Chair)
Qingbo Huang, Ph.D. (Committee Member)
Steen Pedersen, Ph.D. (Committee Member)
198 p.
Applied Mathematics; Mathematics
compressed sensing; frame theory; data-driven; multi-scale; image processing; Parseval relaxation

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Citations

  • Grunden, B. K. (2021). On the Characteristics of a Data-driven Multi-scale Frame Convergence Algorithm [Doctoral dissertation, Wright State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=wright1622208959661057

    APA Style (7th edition)

  • Grunden, Beverly. On the Characteristics of a Data-driven Multi-scale Frame Convergence Algorithm. 2021. Wright State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=wright1622208959661057.

    MLA Style (8th edition)

  • Grunden, Beverly. "On the Characteristics of a Data-driven Multi-scale Frame Convergence Algorithm." Doctoral dissertation, Wright State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=wright1622208959661057

    Chicago Manual of Style (17th edition)

wright1622208959661057
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This open access ETD is published by Wright State University and OhioLINK.