Here's a sagetex solution, not using tikz for blurring the Wikipedia picture. Just find some Python code online, such as from here to find many ways of manipulating your image. I've picked BLUR and CONTOUR.
\documentclass{article}
\usepackage{sagetex}
\usepackage{graphicx}
\begin{document}
Here is the images:\\
\includegraphics[width=2in]{Mona.png}
\begin{sagesilent}
from PIL import Image
from PIL import ImageFilter
from PIL.ImageFilter import (BLUR,CONTOUR)
img = Image.open('Mona.png')
img.filter(BLUR).save('MonaBlur.png')
img.filter(CONTOUR).save('MonaContour.png')
result1 = r"\includegraphics[width=2in]{MonaBlur.png}"
result2 = r"\includegraphics[width=2in]{MonaContour.png}"
\end{sagesilent}
\sagestr{result1}
\sagestr{result2}
\end{document}
The result is shown below, running in CoCalc:

EDIT: Now to handle the partial blurring. From this page I get some instruction on cropping and pasting the cropped image onto another image. I cropped the hands from the original image and pasted them onto the blurred image of the blurred image.
\documentclass{article}
\usepackage{sagetex}
\usepackage{graphicx}
\begin{document}
Here is the images:\\
\includegraphics[width=2in]{Mona.png}
\begin{sagesilent}
from PIL import Image
from PIL import ImageFilter
from PIL.ImageFilter import (BLUR,CONTOUR)
img = Image.open('Mona.png')
Copyimg = img.copy()
croppedIm = img.crop((75, 340, 200, 450))
croppedIm.save('cropped.png')
Copyimg.paste(croppedIm, (0, 0))
img.filter(BLUR).save('MonaBlur.png')
img.filter(CONTOUR).save('MonaContour.png')
img2 = Image.open('MonaBlur.png')
img2.filter(BLUR).save('MonaBlurBlur.png')
img2.paste(croppedIm, (75, 340, 200, 450))
img2.paste(croppedIm, (400, 500))
img2.save('box.png')
result1 = r"\includegraphics[width=2in]{MonaBlur.png}"
result2 = r"\includegraphics[width=2in]{MonaContour.png}"
result3 = r"\includegraphics[width=2in]{box.png}"
result4 = r"\includegraphics[width=2in]{cropped.png}"
\end{sagesilent}
\sagestr{result1}
%\sagestr{result2}
\sagestr{result3}
\sagestr{result4}
\end{document}
The output in CoCalc is now:

The last image is the crop of the hands. This has been pasted onto the spot where it was taken from but now it's on the blurred image. If you click on the image (for a closer view) you will see that the second of the 3 pictures has a fuzzy Mona, except for her hands.
By using Python you get access to a lot of built in commands to manipulate your images.
tikzpicture, or are you wanting to blur parts drawn in TikZ? – Paul Gessler Feb 21 '16 at 14:26