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    Area of Science:

    • Signal Processing
    • Data Compression
    • Applied Mathematics

    Background:

    • Efficient source coding is crucial for data storage and transmission.
    • Existing methods like the Discrete Cosine Transform (DCT) are widely used.
    • Compressive sensing integrates data compression into the acquisition process.

    Purpose of the Study:

    • To develop a novel data compression transform inspired by natural phenomena.
    • To apply this transform within a compressive sensing framework for enhanced data acquisition and reconstruction.
    • To evaluate the performance and robustness of the proposed method compared to existing techniques.

    Main Methods:

    • Constructed real-orthonormal bases from the eigenvectors of vibrating thin square plates, utilizing sinusoidal and hyperbolic functions.
    • Proposed using low-frequency atoms of the Sinusoidal-Hyperbolic Transform (SHT) as sensing patterns in compressive sensing.
    • Formulated a dictionary matrix using SHT and a non-trigonometric sparsifying basis (Hadamard) for well-conditioned pursuit algorithms.

    Main Results:

    • The SHT demonstrated performance comparable to the Discrete Cosine Transform (DCT).
    • The proposed SHT-based compressive sensing method achieved high-fidelity image reconstruction with good encoding/decoding efficiency.
    • Compared to random Gaussian sensing patterns, the SHT method yielded images with significantly higher fidelity at the same compression ratio.
    • The sensing patterns exhibited robustness against Gaussian and Poisson noise.

    Conclusions:

    • The Sinusoidal-Hyperbolic Transform (SHT) provides an effective and efficient approach for data compression and image acquisition.
    • The proposed compressive sensing scheme, utilizing SHT, offers superior reconstruction fidelity and noise robustness.
    • This natural-phenomena-inspired transform presents a promising alternative for efficient data storage and transmission applications.