Sure, open up archive.php and find this code:
<h2><?php /* If this is a category archive */ if (is_category()) { ?>
Archive for <?php echo single_cat_title(); ?>
<?php /* If this is a daily archive */ } elseif (is_day()) { ?>
Archive for <?php the_time('F jS, Y'); ?>
<?php /* If this is a monthly archive */ } elseif (is_month()) { ?>
Archive for <?php the_time('F, Y'); ?>
<?php /* If this is a yearly archive */ } elseif (is_year()) { ?>
Archive for <?php the_time('Y'); ?>
<?php /* If this is a search */ } elseif (is_search()) { ?>
Search Results
<?php /* If this is an author archive */ } elseif (is_author()) { ?>
Author Archive
<?php /* If this is a paged archive */ } elseif (isset($_GET['paged']) && !empty($_GET['paged'])) { ?>
Blog Archives
<?php } ?></h2>
Change it to this:
<h2><?php if (is_category('blog') { ?>
<img src="MY-IMAGE.JPG" alt="MY-DESCRIPTION-OF-THIS-IMAGE" />
<?php /* If this is a category archive */ elseif (is_category() && !is_category('blog')) { ?>
Archive for <?php echo single_cat_title(); ?>
<?php /* If this is a daily archive */ } elseif (is_day()) { ?>
Archive for <?php the_time('F jS, Y'); ?>
<?php /* If this is a monthly archive */ } elseif (is_month()) { ?>
Archive for <?php the_time('F, Y'); ?>
<?php /* If this is a yearly archive */ } elseif (is_year()) { ?>
Archive for <?php the_time('Y'); ?>
<?php /* If this is a search */ } elseif (is_search()) { ?>
Search Results
<?php /* If this is an author archive */ } elseif (is_author()) { ?>
Author Archive
<?php /* If this is a paged archive */ } elseif (isset($_GET['paged']) && !empty($_GET['paged'])) { ?>
Blog Archives
<?php } ?></h2>