db={"collb":[{"_id":1,},{"_id":2,},{"_id":3},{"_id":4}],"colla":[{"_id":1,"someIdsOfB":[1,2]},{"_id":2,"someIdsOfB":[3]}]}

db.collb.aggregate([{"$lookup":{"from":"colla","localField":"_id","foreignField":"someIdsOfB","as":"a"}},{$match:{$expr:{$eq:[{$size:"$a"},0]}}}])