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Lensless Fluorescent Microscopy on a Chip
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High-accuracy total variation with application to compressed video sensing.

Mahdi S Hosseini, Konstantinos N Plataniotis

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |July 3, 2014
    PubMed
    Summary

    This study introduces high-order differential filters for image restoration, overcoming limitations of traditional total variation (TV) methods. The new approach preserves high-frequency details and significantly improves video frame recovery from undersampled data.

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    Area of Science:

    • Signal Processing
    • Image Restoration
    • Computer Vision

    Background:

    • Traditional total variation (TV) regularizers use simple finite-impulse-response (FIR) filters for image restoration.
    • These filters cause texture and geometric loss by distorting high-frequency components crucial for edge information.

    Purpose of the Study:

    • To propose an alternative TV regularization model using high-order accuracy differential FIR filters.
    • To preserve rapid signal transitions and mitigate texture/geometric loss in image and video recovery.

    Main Methods:

    • Developed high-order accuracy differential FIR filters as an alternative to standard TV filters.
    • Designed a numerical encoding scheme for multidimensional (tensorial) representation of the TV model.
    • Applied the model to compressed video sensing for joint frame recovery from undersampled measurements.
    • Utilized alternating direction methods of multipliers for solving the optimization problem, including a unique quadratic minimization step.

    Main Results:

    • The proposed method effectively preserves high-frequency components and rapid signal transitions.
    • Tensorial decomposition enabled regulation of spatial and temporal redundancy in video sensing.
    • The algorithm achieved accurate frame recovery from significantly undersampled measurements.
    • Demonstrated superior performance compared to state-of-the-art methods in both accuracy and visual quality.

    Conclusions:

    • High-order accuracy differential FIR filters offer a superior alternative to standard TV filters for image and video restoration.
    • The tensorial decomposition approach effectively addresses compressed video sensing challenges.
    • The developed algorithm provides significant improvements in restoration accuracy and visual fidelity at lower sampling rates.