This image is peculiar.
At first look, it's just a simple image.
If you shake your head and see it, a face is visible.
How can an image such as this be created (provided I have a bitmap image of a face)?
Here's a way (with no blurring really, but you can add some if you want) I tested and result is not too far from what you want.
Change your guy's face (special credit to Shepard Fairey ;-) to black and white with high contrast (should basically be a "bitmap" image, meaning either black or white, no grey shades).
Apply transparency (10% in my example for a quite obvious result) then place the striped pattern over it. Note I created it in Illustrator using Blend object feature.
That's basically it... Enjoy!
Edit: Huh I didn't read carefully the other answers before posting. This is exactly what Emilie suggested. :-/ Credit goes to her! This is the illustrated version of her answer.
Actually what you are seeing is a filtering issue. See human eyes have different resolutions on different parts of the Retina. In the central focus area you have a denser cluster of sensing cells. Now according to sampling theorem you can not construct an image form data below certain treshold, you get something else.
When you shake your head back and forth your exposing the sides of your eyes to the image, thus artificially reducing your resolution (especially sideways). You can do much the same by moving far away form the monitor or by not looking straight at the image! Now you can exploit this feature by mixing high and low, frequencies of images together (called a hybrid image).
Perhaps the most famous image of this type is the Hybrid image showing albert einstein and marilyn monroe overlaid.
Image 1: Einstein overlaid on marilyn monroe. Showing a more sophisticated version of same illusion. source, look at the image several meters form your monitor to see Einstein disappear
The image in your question is just exploiting the same effect. While overlaying the image is the way do it. But for it to work you must ensure that it is actually a low frequency image. You can in fact design more complex and find more interesting versions of this by using high pass and low pass filtering creatively.
Image 2: Running Gaussian blur (which is a is a low pass filter) on your demo image.
So that is all it is a high frequency banding and a blur resistant shape on top. The blur resistant image is what you see when you remove the contribution of the high frequency image.
You'll need to turn the portrait image into a high constrast image (only black and white with no shades of gray). This can be done by using the Photocopy filter in Photoshop. Before running the filter, make sure your foreground color is a light gray and the background color is white.
On the layer above, create an overlay of black stripes similar to the image you included.
If the portrait on the layer below shows too much, you can try and lower the opacity but not so much that you won't see it anymore when you shake your head.