Add target attribute to image link

functions.php

<?php
//...

function my_add_link_target( $html ) {
	$html = preg_replace( '/(<a.*")>/', '$1 target="_self">', $html );
	return $html;
}
add_filter( 'image_send_to_editor', 'my_add_link_target', 10 );

image-after.html

<a href="http://localhost/jsonapi/wp-content/uploads/2014/11/city-q-c-1024-768-4.jpg" target="_self">
<img src="http://localhost/jsonapi/wp-content/uploads/2014/11/city-q-c-1024-768-4-300x225.jpg" alt="city-q-c-1024-768-4" width="300" height="225" class="alignnone size-medium wp-image-16" />
</a>

image-before.html

<a href="http://localhost/jsonapi/wp-content/uploads/2014/11/city-q-c-1024-768-4.jpg">
<img src="http://localhost/jsonapi/wp-content/uploads/2014/11/city-q-c-1024-768-4-300x225.jpg" alt="city-q-c-1024-768-4" width="300" height="225" class="alignnone size-medium wp-image-16" />
</a>