Here are 2 methods to disable all uploading for users that are not administrators:

Method 1:

Remove the upload_files capability from the roles you do not want to be able to upload.

e.g. removing it from author role:

$role = get_role( 'author' );
$role->remove_cap( 'upload_files' );

This is saved to the database so it should only happen once, not on every page load. Removing it from the editor role should be the same albeit with the obvious modification.

Removing the capability will have the desired effect, but it may have additional effects you may not find so desirable, the only way to be sure is to test

Method 2

Consider this code. It uses the wp_handle_upload_prefilter filter to check the user has admin status, and aborts the upload if they do not. It relies on only administrators and above having manage_options.

<?php
/**
 * Plugin Name: Admin Only Uploads
 * Description: Prevents Uploads from non-admins
 * Author: TJNowell
 * Author URI: https://tomjn.com
 * Version: 1.0
 */

function tomjn_only_upload_for_admin( $file ) {
    if ( ! current_user_can( 'manage_options' ) ) {
        $file['error'] = 'You can\'t upload images without admin privileges!';
    }
    return $file;
}
add_filter( 'wp_handle_upload_prefilter', 'tomjn_only_upload_for_admin' );

You can make use of this filter to be more specific than upload_file, e.g. preventing the upload of images, and only images, but allowing audio, etc