Specific WordPress header by category. This will work for both the category archive page and all individual posts marked with specific categories.

gistfile1.txt

<?php if ( is_front_page() ) : ?><img src="<?php echo get_stylesheet_directory_uri(); ?>/images/specific image for cat">
<?php elseif ( is_category( 'category 1' ) || has_category ('category 1')) : ?>
<img src="<?php echo get_stylesheet_directory_uri(); ?>/images/specific image for cat">
<?php elseif ( is_category( 'category 2' ) || has_category ('category 2')) : ?>
<img src="<?php echo get_stylesheet_directory_uri(); ?>/images/specific image for cat">
<?php elseif ( is_category( 'category 3' ) || has_category ('category 3')) : ?>
<img src="<?php echo get_stylesheet_directory_uri(); ?>/images/specific image for cat">
<?php elseif ( is_category( 'other' ) ) : ?>
<img src="<?php echo get_stylesheet_directory_uri(); ?>/images/specific image for cat">
<?php else: ?>
<img src="<?php echo get_stylesheet_directory_uri(); ?>/images/specific imagge for cat">
<?php endif; ?>