Publication Date
2021
Document Type
Dissertation
Committee Members
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)
Degree Name
Doctor of Philosophy (PhD)
Abstract
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.
Page Count
198
Department or Program
Department of Mathematics and Statistics
Year Degree Awarded
2021
Copyright
Copyright 2021, all rights reserved. My ETD will be available under the "Fair Use" terms of copyright law.
ORCID ID
0000-0002-3088-2601