How to preprocess output of $user_picture in Drupal 7?
In the core user module you can find user-picture.tpl.php. Copy this file to your active theme, edit it and be sure to clear cache.

If you need to go deeper, put this in your theme's template.php. Original can be found in user.module.

function yourthemename_preprocess_user_picture(&amp;$variables) {
  $variables['user_picture'] = '';
  if (variable_get('user_pictures', 0)) {
    $account = $variables['account'];
    if (!empty($account-&gt;picture)) {
      // @TODO: Ideally this function would only be passed file objects, but
      // since there's a lot of legacy code that JOINs the {users} table to
      // {node} or {comments} and passes the results into this function if we
      // a numeric value in the picture field we'll assume it's a file id
      // and load it for them. Once we've got user_load_multiple() and
      // comment_load_multiple() functions the user module will be able to load
      // the picture files in mass during the object's load process.
      if (is_numeric($account-&gt;picture)) {
        $account-&gt;picture = file_load($account-&gt;picture);
      }
      if (!empty($account-&gt;picture-&gt;uri)) {
        $filepath = $account-&gt;picture-&gt;uri;
      }
    }
    elseif (variable_get('user_picture_default', '')) {
      $filepath = variable_get('user_picture_default', '');
    }
    if (isset($filepath)) {
      $alt = t("@user's picture", array('@user' =&gt; format_username($account)));
      // If the image does not have a valid Drupal scheme (for eg. HTTP),
      // don't load image styles.
      if (module_exists('image') &amp;&amp; file_valid_uri($filepath) &amp;&amp; $style = variable_get('user_picture_style', '')) {
        $variables['user_picture'] = theme('image_style', array('style_name' =&gt; $style, 'path' =&gt; $filepath, 'alt' =&gt; $alt, 'title' =&gt; $alt));
      }
      else {
        $variables['user_picture'] = theme('image', array('path' =&gt; $filepath, 'alt' =&gt; $alt, 'title' =&gt; $alt));
      }
      if (!empty($account-&gt;uid) &amp;&amp; user_access('access user profiles')) {
        $attributes = array('attributes' =&gt; array('title' =&gt; t('View user profile.')), 'html' =&gt; TRUE);
        $variables['user_picture'] = l($variables['user_picture'], "user/$account-&gt;uid", $attributes);
      }
    }
  }
}