How to preprocess output of $user_picture in Drupal 7?

By default user picture output markup looks like this:

<div class="user-picture">
    <a href="/user/username" class="active">
        <img class="img-responsive" src="http://www.example.com/sites/example.com/files/styles/profile_page/public/pictures/picture-1-1420552205.jpg?itok=3Kt4fK7H" alt="user avatar username" title="user avatar username" />
    </a>
</div>

I need change markup of user picture output to something like this:

<div class="user-picture">
    <img src="http://www.example.com/sites/example.com/files/styles/profile_page/public/pictures/picture-1-1420552205.jpg?itok=3Kt4fK7H" alt="" />
</div>

Remove unnecessary markup. But question is how?

I have read:

The user-profile.tpl.php file won´t be recognized in my Drupal 7 installation

Changing user picture HTML output on user profile

Will be very appriciate for helping me out.