If you use jQuery, you could try a little workaround to display your images.  
Not a very elegant way, but should work for small projects. 
I started with a little php function to get my newsposts and generate the markup: 
function getNewsfeed(){
  $curl = curl_init();
  curl_setopt_array($curl, array(
    CURLOPT_RETURNTRANSFER => 1,
    CURLOPT_URL => 'http://example.com/service-pages/?template=news&sort=-modified&limit=5'
  ));
  $result = curl_exec($curl);
  curl_close($curl);
  $data = '';
  $result = json_decode($result, true);
  if($result){
    foreach($result[matches] as $news){
      $data .='<div class="js-newsfeedentry s-newsfeedentry">';
      $data .='<h3>'.$news[title].'<small class="pull-right text-muted" style="padding-top:5px">Posted : '.date("d.m.Y - H:i",$news[created]).'</small></h3>';
      $data .= $news[text];
      $data .='<hr />';
      $data .='</div>';
    }
  }
  return $data;
}
as you can see, I wrap the entire newspost into a div with the class "js-newsfeed". 
Now we iterate over all images inside this div and manipulate the img src, to match the correct url from the web-service. 
Inside our document ready function we grab all news images and correct the src: 
 /* fix urls for newsfeed img */
  var newsfeedimg = $('.js-newsfeed img');
  newsfeedimg.each(function(){
    var newimgsrc = 'http://example.com'+$(this).attr('src');
    $(this).attr('src',newimgsrc);
  });
et voila, working images.  
Remember that this isn´t a very good solution because you iterate over every image in your newspost via JavaScript and you shouldn´t do this on a project with many images.