permission for user profile image
The easy way then is to hard code this into your theme.

Open your template.php file in your theme's root folder. Add the following function in that file:

function MYTHEME_preprocess_user_picture(&amp;$vars){
  if (!$vars['logged_in']) {
    // user is anonymous
    $path = variable_get('user_picture_default', FALSE);
    $style = variable_get('user_picture_style', FALSE);
    if ($path &amp;&amp; $style) {
      $vars['user_picture'] = '&lt;img src="' . image_style_url($style, $path) . '" /&gt;';
    }
    else {
      $vars['user_picture'] = '';
    }
  }
}


Replace MYTHEME with the machine name of your theme (similar to the MYTHEME in MYTHEME.info file). Then make sure you add a default picture at:

admin/config/people/accounts


The easiest is to just paste in this in the Default picture text box:

public://default-picture.png


and under the folder sites/default/files include the default-picture.png file. But that is obviously just a suggestion and you can put your picture anywhere.

If you don't see any default picture when viewing the site as anonymous then your default picture path is incorrect. Test it by creating a new user without a picture.