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Learned iterative shrinkage and thresholding algorithm for terahertz sparse deconvolution.

Bo Wang, Xiaoling Qin, Wenping Li

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    Summary
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    A new deep learning method, learned iterative shrinkage and thresholding algorithm (LISTA), enhances terahertz sparse deconvolution for improved defect detection in materials. This faster, more accurate technique aids nondestructive testing.

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    Area of Science:

    • Applied Physics
    • Signal Processing
    • Machine Learning

    Background:

    • Terahertz sparse deconvolution using iterative shrinkage and thresholding algorithm (ISTA) characterizes multilayered structures but is limited to thin samples.
    • ISTA's reliance on precisely extracting convolution matrices from reference signals hinders accuracy, as noise can be mistaken for echoes.
    • Existing methods struggle to distinguish weak echoes from defects in thick materials.

    Purpose of the Study:

    • To propose a novel terahertz sparse deconvolution method, the learned iterative shrinkage and thresholding algorithm (LISTA), for enhanced material characterization.
    • To improve the accuracy and speed of echo estimation compared to traditional ISTA.
    • To enable more effective nondestructive testing of thick samples.

    Main Methods:

    • Developed LISTA by integrating matrix multiplication and soft thresholding into network blocks, forming a deep network architecture.
    • Trained the LISTA network using stochastic gradient descent to optimize convolution matrices for precise echo estimation.
    • Evaluated LISTA on terahertz tomographic imaging of a high-density polyethylene (HDPE) sample.

    Main Results:

    • LISTA demonstrated more precise echo estimation than ISTA.
    • The LISTA algorithm exhibited significantly faster processing speeds, crucial for real-time applications.
    • Improved detection of defects with varying sizes and depths in the HDPE sample was observed.

    Conclusions:

    • LISTA offers superior performance in terahertz sparse deconvolution over ISTA, particularly in accuracy and speed.
    • The developed technique shows significant potential for nondestructive testing of thick materials.
    • LISTA effectively distinguishes weak echoes from minor defects that are often indiscernible with current methods.