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Approximation and compression with sparse orthonormal transforms.

Osman Gokhan Sezer, Onur G Guleryuz, Yucel Altunbasak

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |March 31, 2015
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    Summary
    This summary is machine-generated.

    We developed a new method for designing compression-optimized transforms, called sparse orthonormal transforms (SOTs), which improve signal compression and approximation performance for multimedia applications.

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    Area of Science:

    • Signal Processing
    • Image and Video Compression
    • Multimedia Applications

    Background:

    • Transform compression minimizes signal redundancy by exploiting regularity, crucial for efficient multimedia data handling.
    • Multimedia signals like images and video exhibit diverse localized structures and non-stationary statistics, posing challenges for traditional transform methods.
    • Existing methods often rely on linear approximation or specific signal models, limiting their adaptability to complex signal regularities.

    Purpose of the Study:

    • To introduce a novel transform design method for generating compression-optimized transforms tailored for next-generation multimedia applications.
    • To develop sparse orthonormal transforms (SOTs) that adaptively exploit diverse signal structures and non-stationary statistics.
    • To provide a data-driven, nonlinear approach that extends the capabilities of traditional transforms like the Karhunen-Loeve transform (KLT).

    Main Methods:

    • Design of sparse orthonormal transforms (SOTs) using general nonlinear approximation principles and a data-driven setup.
    • Development of an adaptation method for optimizing transform representation over localized signal regions.
    • An algebraic optimization framework to generate SOTs for various transform structures (multiresolution, block, lapped) and performance targets.

    Main Results:

    • SOT designs demonstrate a principled extension of the KLT, reducing to KLT on Gaussian processes and outperforming it on non-Gaussian statistics.
    • The proposed algebraic optimization framework yields significantly improved n-term approximation performance across different transform structures.
    • Prototype codecs utilizing the new SOTs show consistent increases in compression and approximation performance on image databases compared to conventional methods.

    Conclusions:

    • The proposed SOT design method offers a powerful and flexible approach for creating highly efficient transforms for multimedia compression.
    • This data-driven, nonlinear strategy broadens the applicability of transform coding beyond traditional model-based or linear approximation techniques.
    • The developed SOTs provide superior compression and approximation performance, paving the way for enhanced multimedia applications.