you could use 'body_class()'
http://codex.wordpress.org/Template_Tags/body_class
to generate extra classes, which you might be able to use in the styles of the footer;
or:
you could use conditional statements to create embedded styles in hedader.php.
http://codex.wordpress.org/Conditional_Tags
is_category()
in_category()
just as an example for a possible structure - added to header.php, before </head> :
<style type="text/css" media="screen">
<?php if ( is_category('cat-name1') ) { ?>
#footer { background: #111111 url("<?php bloginfo('stylesheet_directory'); ?>/images/cat1_img.jpg") center top no-repeat; }
<?php } elseif( is_category('cat-name2') ) { ?>
#footer { background: #222222 url("<?php bloginfo('stylesheet_directory'); ?>/images/cat2_img.jpg") center top no-repeat; }
<?php else { ?>
#footer { background: #333333 url("<?php bloginfo('stylesheet_directory'); ?>/images/default_img.jpg") center top no-repeat; }
<?php } ?>
</style>
all depending on the html structure of your theme, and the css id or classes of your footer.
if you use 'is_category()' it will only have effect in the category archives;
if you use 'in_category()' it will have effect in most templates, but you need to consider the if/elseif/else more carefully.