The answer is yes, however it will take months if not years to get it back. I would prune out the green growth in spring (no earlier than April)leaving nothing but the variegated stuff behind, cut as hard as you need to go- spring is an excellent time of year to do so- the plant then has the whole summer to recover- however if more than 50% is removed all at one time the plant will look horrible and it will take a long time to recover, remember a variegated plant grows much more slowly than a plain green one. A local garden to me had one lopped really badly and it took two years to come back to any form of shape- looked really bad- guys had no clue! It looks like it could do with a thinning to me at the back and that will make the plant reshoot- watch for "water shoots/epicormic" growths from the cut off points and make sure that any growth that comes back is the desired stuff you want- anything green gets cut off straight away- wasted energy of the plant if you do leave them- some growths will revert anyway, its normal for an old plant to do that- if lets say its in a dark place or if the plants has been stressed in some way- you could also feed it and water it afterwards to help it , mulch or layer a mix of compost and manure to help recovery too, clearing some of the rubbish from around the plant will help with competition for water, or even possibly pruning some the surrounding plants to allow more sunlight in too might help.