At the time of writing the header image module doesn't support adding header images as a CSS background-image. Instead it simply displays the image field in a header image node. Using CSS background-images is more flexible in many use cases. Yes there are various background image modules but the advantage of using the header image module in this way is its ease of content management and full range of header image display conditions. Most of the other background modules treat non-node pages (views etc) as special cases or don't cover these cases at all or split content management between multiple screens.

So here's how to do it relatively easily with header image.

Install and configure header image

Install and configure header image according to the documentation.

Javascript

In your theme create a new javascript file js/headerimage.js containing the following.

jQuery(document).ready(function($) {

    // Get URL of image in the header image node's image field.
    var imgSrc = $('.block-headerimage .field-image img').attr('src');

    // Set background image of parent block to this image URL.
    $('.block-headerimage').css('background-image', 'url(' + imgSrc + ')');

});

CSS

In your theme create a new CSS file css/headerimage.css containing the following.

/* Styling for header background image */
.block-headerimage {
  background: no-repeat scroll 0px 100% / cover transparent;
  min-height: 200px;
}

/* Hide header image field as it's no longer needed */
.block-headerimage .field-image {
  display: none;
}

Add new files to theme

Edit your theme .info file and add the following lines to include the above CSS and JS.

scripts[] = 'js/headerimage.js'
stylesheets[all][] = 'css/headerimage.css'

Adjust the background-image styling to suit your specific needs. Clear caches, reload your page that contains a header image block and you're done.

Note: The only assumption in the above code is the CSS class of the image field. Here I've used the default ".field-image" that ships in the Drupal 7 standard profile but simplified with fences. If your image field's class is different you'll need to adjust the JS and CSS to match.

Enhancements

Taking it a step further, you can create a new theme region called say hidden, hide the region with CSS display:none and place your header image block in this new hidden region. Then you can adjust the above code to set the CSS background image property of any page element, like say the body tag.

The header image module setup, block placement and authoring experience is the same, but the background image is assigned to exactly the element you want it to be.