Bacteria can be infected by viruses (i.e., “phages”). Bacteria and phages are the most abundant organisms on Earth. Recently, my group has identified patterns in the network of infections amongst viral strains and bacterial strains. However, in many cases, the necessary isolation required to test each possible interaction pair couldn’t be accomplished. Instead, communities of mixed sets of viruses are assayed against communities of mixed sets of hosts. I propose that identifying the pairwise interactions (and their strengths) from such a community-level cross-infection assay represents an interesting and important challenge that may require the methods of compressed sensing and inverse problem theory. I will briefly present the necessary background and problem definition to provoke discussion and, perhaps, further conversations.