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Upsampling01:22

Upsampling

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Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
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Does deblurring improve geometrical hyperspectral unmixing?

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    Area of Science:

    • Spectroscopy
    • Microscopy
    • Image Processing

    Background:

    • Hyperspectral unmixing aims to identify constituent materials in spectral images.
    • Image acquisition processes like microscopy and spectroscopy can introduce blurring, complicating unmixing.
    • Existing geometrical unmixing frameworks may not fully account for blurring effects.

    Purpose of the Study:

    • To investigate the impact of blurring on hyperspectral unmixing within a geometrical framework.
    • To develop a joint observation and mixing model that incorporates blurring.
    • To demonstrate the benefits of deconvolution for improving unmixing accuracy.

    Main Methods:

    • Derivation of a joint observation and mixing model including blurring.
    • Analysis of the model to understand the effect of nonnegative blurring on simplex geometry.
    • Demonstration of the contraction property with a spectrally invariant point-spread function.
    • Application of prior deconvolution techniques.

    Main Results:

    • Nonnegative blurring causes a contraction of the minimum-volume enclosing and maximum-volume enclosed simplex.
    • This contraction impacts end-member identifiability in geometrical unmixing.
    • Prior deconvolution significantly enhances the accuracy of restored sources and abundances.
    • Validation using simulated and real Raman spectroscopic data.

    Conclusions:

    • Blurring in hyperspectral imaging introduces geometric distortions affecting unmixing.
    • A joint model clarifies the relationship between blurring and end-member identifiability.
    • Prior deconvolution is an effective strategy to mitigate blurring effects and improve hyperspectral unmixing results.