add_filter('parse_query', 'own_content_only_restriction' );

function own_content_only_restriction( $wp_query ) {
    if ( !current_user_can( 'see_others_media' ) ) {
        if ( strpos( $_SERVER[ 'REQUEST_URI' ], '/wp-admin/upload.php' ) !== false
        || strpos( $_SERVER[ 'REQUEST_URI' ], '/wp-admin/admin-ajax.php' ) !== false
        || strpos( $_SERVER[ 'REQUEST_URI' ], '/wp-admin/edit.php' ) !== false ) {
            global $current_user;
            $wp_query->set( 'author', $current_user->ID );
        }
    }
}