
The sequence of images with changing grades of blur would need to be prepared with an external software, such as ImageMagick.org. Here, https://ctan.org/lion/files/ctan_lion_350x350.png is used as the source image:
for sigma in {0..10}
do
magick convert ctan_lion_350x350.png -blur 0x$sigma ctan_lion_350x350_blurred_$sigma.png
done
The <sigma> value in the convert option -blur 0x<sigma> may need to be played with for other source images. Bash is used here for convenience to build a loop around convert.
Example document with embedded animation (11 frames at 10 FPS give 1 s of duration)
\documentclass{beamer}
\usepackage{animate}
\usepackage{graphicx}
\begin{document}
\begin{frame}[allowframebreaks]{The \TeX{} Lion blurred}
Go ahead.\\
\framebreak
Here we are:
\begin{center}
\animategraphics[autoplay,width=0.5\linewidth]{10}{ctan_lion_350x350_blurred_}{10}{0}
\end{center}
\end{frame}
\end{document}
animatepackage (works only in Adobe Reader), but you need to make the individual images with various levels of blur yourself. See for example https://tex.stackexchange.com/questions/117543/animation-using-a-sequence-of-images-in-a-single-pdf-file. – Marijn Jan 07 '20 at 14:15