How to chieve the effect

The background looks like a halftone pattern has been applied, the portrait looks a bit like it might have been stippled. 

https://wiki.evilmadscientist.com/StippleGen

Starting with this image.

Make it a Smart Object before doing anything else, so you can go back in and fine tune.

We can get close using Filter Gallery > Sketch > Halftone

Halftone uses the Foreground and Background colours, so make them black and white respectively unless you are going for a 'negative effect.  The dot size is subjective, but try and keep control of the contrast setting at this stage, because tones blown out to full white are essentually lost.

Your example is full black and full white, which you can get using Image > Adjustments > Threshold

The setting is the tonal value above which pixels are made full white, and below which, full black.  Not very subtle.

You might prefer to use a Curves layer and have more control over tonal values, which will let you retain more detail.

Note that the effects are listed under the Smart Object mask. This lets you turn an effect off (as I have done with the unwanted Threshold adjustment).  You can also double click the Filter Gallery (which is the halftone) and adjust the settings.  It's all completely nondestructive, and better way to work.  I have set the curve so that there some dark greys so we can see detail in the hair, by example.  It's entirely up to you and the exact effect you are going for.

Don't forget that the Smart Object and Curves layer both have masks.  You can mask their effect by painting with a black brush in the mask.