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Low-Complexity Multidimensional DCT Approximations for High-Order Tensor Data Decorrelation.

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    New low-complexity multidimensional discrete cosine transform (DCT) approximations offer significant computational savings for video coding and visual tracking. These methods achieve comparable performance to exact 3D DCT with fewer operations.

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    Area of Science:

    • Digital Signal Processing
    • Image and Video Processing
    • Computational Mathematics

    Background:

    • The Discrete Cosine Transform (DCT) is fundamental in signal and image compression.
    • High-dimensional DCT, particularly 3D DCT, is computationally intensive, limiting its application.
    • Efficient approximations are needed to reduce computational complexity in multidimensional signal processing.

    Purpose of the Study:

    • To develop low-complexity approximations for multidimensional Discrete Cosine Transforms (DCT).
    • To formalize these approximations using high-order tensor theory for general dimensions.
    • To evaluate the computational cost and performance of these approximations in video coding and visual tracking.

    Main Methods:

    • Formalization of 3D DCT approximations using high-order tensor theory.
    • Development of several multiplierless 8x8x8 approximate DCT methods.
    • Integration of approximate 3D DCT into a video coding scheme with modified quantization.
    • Application of approximate 3D DCT in a visual tracking system.

    Main Results:

    • The proposed approximate methods exhibit considerably lower computational complexity than the exact 3D DCT.
    • Video coding using approximate 3D DCT yields visual quality nearly identical to the exact 3D DCT.
    • The approximate 3D DCT-based visual tracking system performs comparably to the exact 3D DCT method.
    • Demonstrated competitive performance at a significantly reduced computational cost.

    Conclusions:

    • Low-complexity multidimensional DCT approximations are feasible and effective.
    • These approximations maintain high visual quality in video coding applications.
    • Approximate 3D DCT is a viable tool for efficient visual tracking.
    • The proposed methods offer a practical trade-off between computational cost and performance.