jQuery Submit Form (w/ file and text) without redirecting from current window

I want to build an application form where on can attach an image - it's just a couple of input elements - within a div (not an form element). The form shall be processed without an page redirect. So I use ajax. Everything works fine so far. But now I need to add an image.

$('#submit_application').click(function () {
//...
    $.ajax({
        url: 'submit.php',
        type: 'post',
        data: {
            'action': 'submit',
            'image': $('#image_upload').val(),
             // ..
            'someStringifiedJSON': JSON.stringify(foo)
        },
        success: function (data, status) {
            // ...
        },
        error: function (xhr, desc, err) {
            // ...
        }
    });
});

How can I get my file into php's $_FILES variable? Or how can I pass the file to php so that I can upload it?