Hirschman Transform Applications in Compressive Sensing
The CS technology has attracted considerable attention because it can surpass the traditional limit of Nyquist sampling theory. Rather than sampling a signal at a high frequency and then compressing it, the CS senses the target signal in a compressed format directly. However, the g...
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| Format: | Others |
| Language: | English English |
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Florida State University
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| Online Access: | http://purl.flvc.org/fsu/fd/FSU_FALL2017_XI_fsu_0071E_14193 |
| Summary: | The CS technology has attracted considerable attention because it can surpass the traditional limit of Nyquist sampling theory. Rather
than sampling a signal at a high frequency and then compressing it, the CS senses the target signal in a compressed format directly. However,
the great sampling improvement results in the increased complexity in decoding. The optimization of sensing structure never stops to simplify
the decoding procedure as much as possible. Unlike the Heisenberg-Weyl measure, the Hirschman notion of joint uncertainty is based on entropy
rather than energy. The Discrete Hirschman Transform (DHT) has been proved to be superior in complexity reduction and high resolution to the
traditional Discrete Fourier Transform in many aspects such as fast filtering, spectrum estimation, and image identification. In this
dissertation, I implement a new deterministic compressive sensing system based on DHT with four contributions: (1) apply Weyl's sum character
estimation to the DHT matrices to develop a new deterministic sensing structure (2) theoretically prove that the new sensing structure
satisfy the Mutual Incoherence Property (3) discover a Non-tensor Wavelet Transform as the sparse basis for DHT sensing structures as well as
for other DFT and DFT-like sensing matrices. (4) design a DHT computational core based on FPGA and related communication suite based on
C#. === A Dissertation submitted to the Department of Electrical and Computer Engineering in partial fulfillment of
the requirements for the degree of Doctor of Philosophy. === Fall Semester 2017. === November 14, 2017. === Deterministic Sensing Structures, DHT computational core, Discrete Hirschman Transform, Non-tensor Wavelet === Includes bibliographical references. === Victor E. DeBrunner, Professor Directing Dissertation; Kyle A. Gallivan, University Representative;
Bruce A. Harvey, Committee Member; Linda DeBrunner, Committee Member; Rodney Roberts, Committee Member. |
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