Unfortunately, you can't do that with MongoDB in a single step on the database server. You'll need to do it client side.
While you can project (documentation) your results to only include/exclude some fields (or the first matching result in an array for example as shown here), you can't conditionally do it based on a search with multiple arrays (and the projection operator returns only the first match, not just the results that match).
You might need to consider a different document/collection structure to meet your requirements. MongoDB doesn't have sub-document level filtering/searching yet.