[{"_id":1,"name":"some person","hobbies":[{"name":"A","description":"AB","notImportantField":"ABCDEF"},{"name":"ABC","description":"ABCD","notImportantField":"ABCDEF"}]}]

db.collection.aggregate([{$match:{_id:1}},{"$addFields":{hobbies:{$filter:{input:"$hobbies",cond:{$or:[{$regexMatch:{input:"$$this.name",regex:"d",options:"i"}},{$regexMatch:{input:"$$this.description",regex:"d",options:"i"}}]}}}}}])