What software can create a photo mosaic portrait from multiple images?

The technique is called a photomosiac, where an image in composed of lots of smaller images with different overall colour / brightness such that it resembles the master image when viewed from a distance.

There exist many pieces of software to sort the images and build the mosaic for you. That's not the hard part.

The problem is that if you have, say 20 images, you're only going to be able to represent the face as a 4x5 grid of pixels (unless the software is able to exploit the shapes with an image, and you get extremely lucky with your source images).

This is what a 4 pixel by 5 pixel image looks like:

Could be a pork chop.

If you quadruple the number of images then you get something like this:

Which is at least recognisable as a human face.

But to stand a chance of being able to recognise the image, you need something more like 20x25:

But that's a very famous face, personally I would recommend going a little bit higher, 32x40:

And then everybody knows who the portrait is of. 32x40 requires 1280 images. But that's if there just so happens to be the exact number of each colour/brightness required in the collection. In reality this wont happen so you need to multiply by a factor of 4, or more, meaning realistically you should be looking at 4,000 images. So I think you're going to struggle with 20.