Hirschman Transform Applications in Compressive Sensing

• Other Authors: Xi, Peng (author)
• Format: Others
• Language: English; English
• Published: Florida State University
• Subjects: Electrical engineering; Engineering
• Online Access: http://purl.flvc.org/fsu/fd/FSU_FALL2017_XI_fsu_0071E_14193

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.