Is it possible to re-focus (recover) an intentionally blurred image?

No, the detail is lost and a JPEG does not contain 'history' to allow the blurring to be undone.

Try it: save an image with the faces blurred as a JPEG, then re-open it and try to recover the detail.

If the information has been lost the information has been lost, BUT a skilled user could easily enough add in "data" from other face images and reconstruct your image so that it looks like the face belongs.

If you're doing this for security or privacy, the only sure way is to really mask out the faces with solid color. A sufficient amount of blur will be destructive, to the point where reconstruction techniques like deconvolution won't be effective — but if the image will be subject to scrutiny, it might be hard to judge how much is needed to be safe. Which means that the safe thing to do is use a solid overlay rather than something which is inherently based on the underlying data.

Certainly don't use a filter like mosaic or distortion; it's sometimes amazing how well these can be reversed.

I work in data security and follow some data security news, images with data hidden by bluring and other image manipulation are "broken" all the time.

Digital filters in software work by taking the image data, doing some math on it and producing the modified image.

Unlike images that are shot out of focus in camera, with digitally blured images we know exactly the math formula the software used - and often we can reverse the formula and get the original image back (sometimes with some quality loss)

I have no idea what Picasa soft focus uses and I don't know if it's reversible, also I'm not going to analyze it, treat this answer as a general warning not as a review of Picasa'a soft focus filter's security

Even if we can't un-blur the image often it's possible to recognize the blured person/object/text/whatever by bluring sections from other images and comparing them (because if we take two similar image and apply the same math to both we get two similar changed images).

So, your bluring method will stop the casual surfer but not anyone who really want to get the data, never use it to hide really sensitive data (especially not text or numbers), be careful and if you want to hide something just paint over it with a solid color (and check it's also hidden in thumbnails, preview images, undo histories and such).

The short answer is a loud NO. What you are asking is equvivalent with me giving you a number, lets say, 10000, and I ask you what summation this number is a result of, lets say 5000 + 5000. There is 4999 other possibilities, thus there is no way you can calculate this, but are limited to wild guesses. A blurry image is essentially polluted by light from adjacent points in the object to adjacent pixels in the sensor. Thus every point in the image is a sum of many points in the object.

Though, there is not zero information about the object in a blurry image. For instanse, if you had another image of the same object (face) you can run different digital filters to get answer to this question: could this blurry image be of the same person I've got another, sharp image? This is basically the technique being used by people who claim they can reconstruct lost information in an image. They assume stuff about the object.

If the answer is yes, it wouldn't prove it is the same face because a blurry image would fit almost unlimited amount of faces, depending how blurry the image is.

This is the reason why photographers, good ones I might add, stress the point: you can never recover lost information in post production. You can only post produce a new image from an image you dislike so that it looks good according to certain emotional driven standards, but it has nothing to do with the object.