Laravel Collection get unique values from nested datastructure

I want to use Laravel 5.1 Collection's Unique method to filter unique IDs from nested objects.

Given the data structure

{
  "key1": [
    {"id": 1},
    {"id": 1}
  ],
  "key2": [
    {"id": 1},
    {"id": 2}
  ]
}

I want to return the same datastructure with duplicate id 1 removed from "key 1".

I wanted to use $unique = $collection->unique('id');, but this doesn't seem to apply to a nested datastructure as I have.

So I thought to use $collection

    $input = $request->all();

    $collection = collect($input);

    $collection->each(function($obj, $key) {
        //$key is "key1", "key2"
        //obj is the associated array of objects containing IDs
    })->unique('id');

I don't quite know how to structure this.

The result structure should be:

{
  "key1": [
    {"id": 1}
  ],
  "key2": [
    {"id": 1},
    {"id": 2}
  ]
}

via Chebli Mohamed