Json.Net: How to stop empty elements to be converted as somenode:null while converting XML to JSON

I am using Newton Json.net library to convert XML to JSON. My XML sample is

<space>
<frame>
  <photo img="cakecollage1.jpg" />
  <text string="Browse my cake space" />
  <rule type="F" img="cakecollage9.jpg" x="150" y="0" w="300" h="250" />
  <rule />
</frame>
<frame>
  <photo img="cakecollage2.jpg" />
  <rule/>
  <rule/>
</frame>
</space>

Following code is written to convert it to Json.

XmlDocument doc = new XmlDocument();
doc.Load("Doc.xml");

string json = JsonConvert.SerializeObject(doc, new Newtonsoft.Json.JsonSerializerSettings() {NullValueHandling = NullValueHandling.Include, MissingMemberHandling = MissingMemberHandling.Ignore });

And the OUTPUT is :

{
  "space": {
    "frame": [
      {
        "photo": {
          "@img": "cakecollage1.jpg"
        },
        "text": {
          "@string": "Browse my cake space"
        },
        "rule": [
          {
            "@type": "F",
            "@img": "cakecollage9.jpg",
            "@x": "150",
            "@y": "0",
            "@w": "300",
            "@h": "250"
          },
          null
        ]
      },
      {
        "photo": {
          "@img": "cakecollage2.jpg"
        },
        "rule": [
          null,
          null
        ]
      }
    ]
  }
}

My requirement is that the OUTPUT should not contain any null values. I mean I don't want

"rule": [
          null,
          null
        ]

at all in my object. Wherever empty node is there in XML, that element should not be converted.

Thanks in advance, Satya