You will need a process to ...

You will need a process to oxidize and flocculate these particles. 

Separation can then be through a membrane system. A scale will form on the membrane which will need to be managed through chemical cleaning.

Another alternative, although not tested for strontium and barium, could be using hydrodynamic cavitation combined with Activated Filter Media. The hydrodynamic cavitation through a static mixer will raise the oxidation potential of the water and help with flocculation. The activated filter media uses electrostatic attraction instead of the conventional physical attachment in the case of sand and zeolitic materials. Removal efficiencies are typically between 1 to 5 micron with 99% efficiency. 

My company is experienced with this process and have successfully removed iron, manganese, aluminium, arsenic, chromium from water. If you are able to send a water sample, we can both work collaboratively to provide a solution.

Please email me at andrew@waterandoilsolutions.com.au