Upload thumbnail post type frontend via AJAX

Question

I have a professional registration form, where the same register entering name and image (photo). This registration without the use of Ajax, I can do, but it must be done in Ajax, and the image I can not send, even using formData. Follow below as is my code at the moment.

page-Register.php

<form id="form-professionals">
  <input type="text" id="name" name="name" required placeholder="Insert the Name" value=""/>
  <input type="file" name="image" id="image">
  <button id="button-register-professionals">Register</button>
  <div class="notification-profesionals"></div>

js scripts.

$(document).ready(function () {
$('#button-register-professionals').click(function () {
    var name = $('#name').val();
    var image = $('#image').val();
    if (name == '') {
        alert('Required Field');
    } else {
        $.ajax({
            type: 'POST',
            url: ajaxurl,
            data: {
                action: 'register_professionals',
                name: name,
                image: image
            },
            success: function (response) {
                $('.notification-profesionals').html(response);

            },

            error: function (response) {
                console.log('error: ' + response);
            }
        });
    }
    return false;
});});

functions.php

add_action('wp_ajax_nopriv_register_professionals', 'register_professionals');
add_action('wp_ajax_register_professionals', 'register_professionals');

function register_professionals(){
$post_type = 'professionals';
$title = $_POST['name'];
$image = $_FILES['image'];


$new_post = array(
    'post_title' => $title,
    'post_status' => 'pending',
    'post_type' => $post_type,

);

wp_insert_post($new_post);

if (!function_exists('wp_generate_attachment_metadata')) {
    require_once(ABSPATH . "wp-admin" . '/includes/image.php');
    require_once(ABSPATH . "wp-admin" . '/includes/file.php');
    require_once(ABSPATH . "wp-admin" . '/includes/media.php');
}
if ($image) {

    foreach ($image as $file => $array) {
        if ($image[$file]['error'] !== UPLOAD_ERR_OK) {
            return "upload error : " . $image[$file]['error'];
        }
        $attach_id = media_handle_upload($file, $id);
    }
} else {
    echo 'error - image';
}
if ($attach_id > 0) {
    update_post_meta($id, '_thumbnail_id', $attach_id);
    echo 'success - add image';

} else {
    echo 'error - add image';
}

if ($id) {
    echo 'Success';
} else {
    echo 'Error';
}
die();
}