[{review:[{title:"Title1",professor:[{id:"1",accept:false},{id:"2",accept:false}]}]},{review:[{title:"Title2",professor:[{id:"3",accept:false},{id:"2",accept:false}]}]}]

db.collection.aggregate([{"$match":{review:{$elemMatch:{professor:{$elemMatch:{id:"1"}}}}}},{"$unwind":"$review"},{$project:{review:{title:1,professor:{$filter:{input:"$review.professor",as:"professor",cond:{$eq:["$$professor.id","1"]}}}}}}])