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Alfred S. Carasso and Andras E. Vladar develop a mathematical method for sharpening electron-microscope images without knowing the original blur in advance. Their approach uses Linnik probability densities and a time-reversed diffusion equation to reconstruct detail from suitable images.
The report explains the Fourier-space formulation, the restrictions on images to which it applies and the selection of a partial rather than total deconvolution. Original and processed images illustrate the behaviour of the method for scanning electron and helium-ion microscopy. Equations, Fourier spectra, parameter values and references are preserved in this complete original technical note, dated December 2024 and released by NIST in January 2025.
The Whirlpool Galaxy comparison uses an image credited to T. A. Rector and Monica Ramirez/NOIRLab/NSF/AURA, distributed under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/. The report’s original deblurring comparisons remain unchanged.
Alfred S. Carasso; Andras E. Vladar. Linnik Point Spread Functions, Time-Reversed Logarithmic Diffusion Equations, and Blind Deconvolution of Electron Microscope Imagery. National Institute of Standards and Technology, 2024. https://doi.org/10.6028/NIST.TN.2324. Complete original publication and source credits retained.
Astronomical image source: https://www.astropix.org/image/noirlab/noao0124a. Credit: T. A. Rector and Monica Ramirez/NOIRLab/NSF/AURA. CC BY 4.0. Original and NIST-processed comparisons retained as published.