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Compressive Estimation and Imaging Based on Autoregressive Models.

Matteo Testa, Enrico Magli

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    This study introduces a new framework for compressive estimation of autoregressive (AR) process parameters. The novel techniques improve compressive covariance estimation and block-based compressive imaging systems.

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    Area of Science:

    • Signal Processing
    • Information Theory
    • Statistical Inference

    Background:

    • Compressed sensing (CS) enables efficient signal acquisition but direct information extraction from measurements is challenging.
    • Recovering signals from CS measurements is computationally intensive, motivating direct estimation methods.

    Purpose of the Study:

    • To develop a novel framework for compressive estimation of autoregressive (AR) process parameters.
    • To address challenges in compressive covariance estimation and block-based compressive imaging.

    Main Methods:

    • Proposed a compressive least squares estimator for AR(p) parameters.
    • Introduced a compressive Bayesian estimator for AR(1) parameters.
    • Developed parametric and adaptive algorithms for specific applications.

    Main Results:

    • Achieved improved compressive covariance estimation for Toeplitz matrices.
    • Enhanced block-based compressive imaging with adaptive measurement acquisition.
    • Demonstrated superior performance over state-of-the-art methods.

    Conclusions:

    • The proposed framework offers an effective approach for direct information estimation from compressed signals.
    • Novel techniques significantly advance the capabilities of compressive sensing in practical applications.