Currently there's no way to use pattern match in $filter or $cond operators. Pattern match is most frequently used filtering/conditional methodologies
It seems quite disappointing that there are restrictions on using conditions while the sole purpose of $filter & $cond are to filtering out result set. Sample query is given below. I'm not putting similar code on $cond since it looks same. It would be nice if we can do something like below:

// Some comments here
{
  $filter: {
     input: "$Restaurants",
     as: "restaurant",
     cond: { "$$restaurant":{$regex: "valley"} }
  }
}