I'm a water treatment engineer. Carbon filtration will remove dissolved solids and heavy metals, and with high efficiency if done correctly. Most GAC columns designed to remove lead and heavy metals are enriched with sulfide ions to increase the removal efficiency as well. People prefer to use ion exchange resins to remove heavy metals because they can be regenerated more easily and efficiently. Also ion exchange resins allow you to recover any absorbed minerals.
http://ascelibrary.org/doi/10.1061/%28ASCE%290733-9372%28199...