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    Strategies for Sparsity-based Time-Frequency Analyses

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    Genre
    Thesis/Dissertation
    Date
    2021
    Author
    Zhang, Shuimei cc
    Advisor
    Zhang, Yimin
    Committee member
    Silage, Dennis
    Picone, Joseph
    Aviyente, Selin
    Department
    Electrical and Computer Engineering
    Subject
    Electrical engineering
    Burst missing samples
    Crossterm mitigation
    Deep neural network
    Low-rank structured matrix completion
    Nonstationary signal
    Time-frequency analysis
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/6457
    
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    DOI
    http://dx.doi.org/10.34944/dspace/6439
    Abstract
    Nonstationary signals are widely observed in many real-world applications, e.g., radar, sonar, radio astronomy, communication, acoustics, and vibration applications. Joint time-frequency (TF) domain representations provide a time-varying spectrum for their analyses, discrimination, and classifications. Nonstationary signals commonly exhibit sparse occupancy in the TF domain. In this dissertation, we incorporate such sparsity to enable robust TF analysis in impaired observing environments. In practice, missing data samples frequently occur during signal reception due to various reasons, e.g., propagation fading, measurement obstruction, removal of impulsive noise or narrowband interference, and intentional undersampling. Missing data samples in the time domain lend themselves to be missing entries in the instantaneous autocorrelation function (IAF) and induce artifacts in the TF representation (TFR). Compared to random missing samples, a more realistic and more challenging problem is the existence of burst missing data samples. Unlike the effects of random missing samples, which cause the artifacts to be uniformly spread over the entire TF domain, the artifacts due to burst missing samples are highly localized around the true instantaneous frequencies, rendering extremely challenging TF analyses for which many existing methods become ineffective. In this dissertation, our objective is to develop novel signal processing techniques that offer effective TF analysis capability in the presence of burst missing samples. We propose two mutually related methods that recover missing entries in the IAF and reconstruct high-fidelity TFRs, which approach full-data results with negligible performance loss. In the first method, an IAF slice corresponding to the time or lag is converted to a Hankel matrix, and its missing entries are recovered via atomic norm minimization. The second method generalizes this approach to reduce the effects of TF crossterms. It considers an IAF patch, which is reformulated as a low-rank block Hankel matrix, and the annihilating filter-based approach is used to interpolate the IAF and recover the missing entries. Both methods are insensitive to signal magnitude differences. Furthermore, we develop a novel machine learning-based approach that offers crossterm-free TFRs with effective autoterm preservation. The superiority and usefulness of the proposed methods are demonstrated using simulated and real-world signals.
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