Carasso, A.
and Vladar, A.
(2025),
Linnik Point Spread Functions, Time-Reversed Logarithmic Diffusion Equations, and Blind Deconvolution of Electron Microscope Imagery, Technical Note (NIST TN), National Institute of Standards and Technology, Gaithersburg, MD, [online], https://doi.org/10.6028/NIST.TN.2324, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=959180
(Accessed January 8, 2025)
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Linnik Point Spread Functions, Time-Reversed Logarithmic Diffusion Equations, and Blind Deconvolution of Electron Microscope Imagery
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Abstract
Abstract. A non-iterative direct blind deconvolution procedure, previously used successfully to sharpen Hubble Space Telescope imagery, is now found useful in sharpening nanoscale scanning electron microscope (SEM) and helium ion microscope (HIM) images. The method is restricted to images g(x, y), whose Fourier transforms ĝ(ξ, η) are such that log |ĝ(ξ, 0)| is globally monotone decreasing and convex. The method is not applicable to defocus blurs. A point spread function in the form of a Linnik probability density function is postulated, with parameters obtained by least squares fitting the Fourier transform of the preconditioned microscopy image. Deconvolution is implemented in slow motion by marching backward in time, in Fourier space, from t = 1 to t = 0, in an associated logarithmic diffusion equation. Best results are usually found in a partial deconvolution at time t̄, with 0 < t̄ < 1, rather than in total deconvolution at t = 0. The method requires familarity with microscopy images, as well as interactive search for optimal parameters.Citation
Technical Note (NIST TN) - 2324
Report Number
2324
NIST Pub Series
Pub Type
NIST Pubs
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Keywords
Key words. SEM images, HIM images, sharpening, denoising, deblurring, blind deconvolution, Linnik point spread functions, time-reversed logarithmic diffusion equations.
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Created January 2, 2025, Updated January 6, 2025