How to remove white border from blur background image

The simplest way to do it is by adding transform: scale(1.1). Try it here.

#overlay {
 position: fixed;
 left: 22.5em;
 top: 3em;
 height: 75%;
 width: 50%;
 background: url("https://s-media-cacheak0.pinimg.com/originals/ae/b4/c5/aeb4c53cab2b550187644af503a0f17e.png");
 background-size: cover;
 filter: blur(9px);
 transform: scale(1.1); 
}

I have added overflow, padding and even margin, but still the problem not solved. So i tried to give the image tag between div. Problem solved.

<div class="background-image">
<img src="http://www.hdpaperz.com/wallpaper/original/windows-8-wallpapers-2560x1600-2311_1.jpg" width="100%" height="100%"/>
</div>

css

 .background-image {
  background: no-repeat center center fixed; 
  background-size: cover;
  display: block;
  left: -5px;
  top:-5px;
  bottom:-5px;
  position: fixed;
  right: -5px;
  z-index: 1;
  -webkit-filter: blur(5px);
  -moz-filter: blur(5px);
  -o-filter: blur(5px);
  -ms-filter: blur(5px);
  filter: blur(5px);
  -webkit-background-size: cover;
  -moz-background-size: cover;
  -o-background-size: cover;
  margin:-5px;

 }

js fiddle

http://jsfiddle.net/2pgdttLh/

Up-to-date answer (2022)

You can achieve this effect with just css by using backdrop-filter on an overlaying element.

.blurred::after {
  content: "";
  position: absolute;
  width: 100%;
  height: 100%;
  backdrop-filter: blur(10px); /* apply the blur */
  pointer-events: none; /* make the overlay click-through */
}

.blurred {
  position: relative;
  width: 500px;
  height: 300px;
  background: no-repeat center center;
  background-image: url('https://besthqwallpapers.com/Uploads/26-5-2019/94041/thumb2-tesla-model-x-2019-exterior-front-view-new-gray-model-x.jpg');
  background-size: cover;
}

<div class="blurred"></div>

Update (8-8-2022): This is now also fully supported in Firefox