Custom Category Image – Got that to work, but can't get it to link to it's URL

I was able to create a custom image for each category on my site here: http://www.pinkfloydonline.com – (Notice the purple arrows that say “Pink Floyd News” and “Pink Floyd Video of the Week”.

Now I am trying to get it to link to it’s category, but can’t seem to get it to work.

Here is the code I used for the custom image:

<?php
foreach((get_the_category()) as $category) {
    echo '<img src="http://pinkfloydonline.com/images/' . $category->cat_ID . '.png" alt="' . $category->cat_name . '" title="' . $category->cat_name . '" />';
}
?>

I looked at the codex and tried adding <?php get_category_link( $category_id ); ?> like this:

<?php
foreach((get_the_category()) as $category) {
    echo '<a href="<?php get_category_link( $category_id ); ?>"><img src="http://pinkfloydonline.com/images/' . $category->cat_ID . '.png" alt="' . $category->cat_name . '" title="' . $category->cat_name . '" /></a>';
}
?>

But it didn’t work.

Any ideas?