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Differential leveling is a precise method in surveying used to determine the elevation difference between two points. Its primary goal is to establish accurate vertical measurements to create level surfaces or grade lines critical for designing and constructing infrastructures such as roads, bridges, and buildings.The procedure for differential leveling begins with setting up and leveling the instrument at a point where the benchmark can be seen. The level rod is held on the benchmark (BM), and...
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Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
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Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

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Generalized higher degree total variation (HDTV) regularization.

Yue Hu, Greg Ongie, Sathish Ramani

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |April 9, 2014
    PubMed
    Summary
    This summary is machine-generated.

    We introduce generalized higher degree total variation (HDTV) for improved image regularization. This novel method significantly enhances image quality in medical and microscopy imaging compared to traditional total variation (TV).

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    Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
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    Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

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    Area of Science:

    • Image processing and computational imaging.
    • Mathematical optimization and regularization techniques.

    Background:

    • Total Variation (TV) is a popular image regularization penalty.
    • Existing higher degree total variation (HDTV) methods extend TV using higher-order derivatives.
    • Further generalization of HDTV is needed for broader applicability.

    Purpose of the Study:

    • Introduce generalized higher degree total variation (HDTV) penalties.
    • Extend existing HDTV methods to incorporate more complex image derivatives.
    • Develop a fast algorithm for image recovery problems using generalized HDTV regularization.

    Main Methods:

    • Proposed a family of generalized higher degree total variation (HDTV) regularization penalties.
    • Developed a novel fast alternating minimization algorithm for solving image recovery problems.
    • Validated the method on 3D magnetic resonance images and 3D microscopy images.

    Main Results:

    • Generalized HDTV penalties encompass many second-degree TV extensions.
    • The new alternating minimization algorithm achieves a tenfold speed improvement over previous methods.
    • HDTV and generalized HDTV significantly improve image quality compared to standard TV regularization.

    Conclusions:

    • Generalized HDTV offers enhanced image regularization capabilities.
    • The proposed fast algorithm enables efficient image recovery with HDTV.
    • These advancements lead to substantial improvements in image quality for medical and scientific imaging applications.